The laws of indicesare fundamental rules for working with... Show more
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8
0
abi
01/09/2025
Arithmetic
Index Laws
390
•
1 Sept 2025
•
Master the 8 and 9 Laws of Indices: Easy Examples and Fun Worksheets
abi
@lvjyabi
Worked Examples: Applying Index Laws
This page demonstrates practical applications of the laws of indices through worked examples. These examples illustrate how to use the laws to simplify complex expressions.
The first example shows:
m^4 × m^2 = m^6
This utilizes the addition law of indices, where exponents with the same base are added.
Another example presented is:
3r^3 × 5r^4 × 2r^8 = 30r^15
Example: In this case, we multiply the coefficients (3 × 5 × 2 = 30) and add the exponents of r (3 + 4 + 8 = 15).
These worked examples help reinforce the understanding of how to apply index laws in various scenarios, which is crucial for mastering algebraic manipulation.
Highlight: Practicing with diverse examples is key to becoming proficient in using index laws.
Advanced Index Law Applications
This page delves into more complex applications of the laws of indices, showcasing how they can be used to solve more intricate problems.
One of the examples presented is:
12n^10 ÷ n^2 = n^8
This demonstrates the subtraction law of indices, where exponents are subtracted when dividing terms with the same base.
Another example shown is:
15n^12 ÷ 3n^6 = 5n^6
Example: Here, we divide both the coefficients (15 ÷ 3 = 5) and subtract the exponents (12 - 6 = 6).
These examples illustrate how index laws can be applied to simplify fractions and complex algebraic expressions.
Highlight: The ability to manipulate expressions using index laws is a crucial skill in advanced algebra and calculus.
Complex Index Manipulations
The final page presents more advanced applications of the laws of indices, demonstrating their use in complex mathematical expressions.
One example shown is:
(m^24)^9 = m^216
This utilizes the multiplication law of indices, where the exponents are multiplied when a power is raised to another power.
Another example is:
(3r^2)^4 = 81r^8
Example: In this case, we raise both the base number and the variable to the power of 4: 3^4 = 81 and (r^2)^4 = r^8.
These examples showcase how index laws can be applied to solve complex problems involving nested exponents and multiple variables.
Highlight: Mastering these complex manipulations is essential for success in higher-level mathematics courses.
The page also includes additional examples that further reinforce the application of various index laws in different scenarios.
Index Laws: Addition and Multiplication
The first page introduces two fundamental laws of indices: the addition law and the multiplication law. These laws are essential for simplifying expressions involving exponents.
Definition: Index laws are rules that govern how to manipulate expressions with exponents.
The page presents three key laws:
- Addition of powers: y^a × y^b = y^(a+b)
- Subtraction of powers: y^a ÷ y^b = y^(a-b)
- Multiplication of powers: (y^a)^b = y^(a×b)
Example: Using the addition law, we can simplify x^3 × x^4 to x^7 because 3 + 4 = 7.
These laws form the foundation for more complex operations with indices and are crucial for solving algebraic equations efficiently.
Highlight: The multiplication law of indices is particularly useful in simplifying nested exponents.
We thought you’d never ask...
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Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
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4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Master the 8 and 9 Laws of Indices: Easy Examples and Fun Worksheets
abi
@lvjyabi
The laws of indices are fundamental rules for working with exponents in mathematics. These rules simplify calculations involving powers and are essential for algebra and higher mathematics.
- Eight key laws of indices cover addition, subtraction, multiplication, and division of powers... Show more
Worked Examples: Applying Index Laws
This page demonstrates practical applications of the laws of indices through worked examples. These examples illustrate how to use the laws to simplify complex expressions.
The first example shows:
m^4 × m^2 = m^6
This utilizes the addition law of indices, where exponents with the same base are added.
Another example presented is:
3r^3 × 5r^4 × 2r^8 = 30r^15
Example: In this case, we multiply the coefficients (3 × 5 × 2 = 30) and add the exponents of r (3 + 4 + 8 = 15).
These worked examples help reinforce the understanding of how to apply index laws in various scenarios, which is crucial for mastering algebraic manipulation.
Highlight: Practicing with diverse examples is key to becoming proficient in using index laws.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Advanced Index Law Applications
This page delves into more complex applications of the laws of indices, showcasing how they can be used to solve more intricate problems.
One of the examples presented is:
12n^10 ÷ n^2 = n^8
This demonstrates the subtraction law of indices, where exponents are subtracted when dividing terms with the same base.
Another example shown is:
15n^12 ÷ 3n^6 = 5n^6
Example: Here, we divide both the coefficients (15 ÷ 3 = 5) and subtract the exponents (12 - 6 = 6).
These examples illustrate how index laws can be applied to simplify fractions and complex algebraic expressions.
Highlight: The ability to manipulate expressions using index laws is a crucial skill in advanced algebra and calculus.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Complex Index Manipulations
The final page presents more advanced applications of the laws of indices, demonstrating their use in complex mathematical expressions.
One example shown is:
(m^24)^9 = m^216
This utilizes the multiplication law of indices, where the exponents are multiplied when a power is raised to another power.
Another example is:
(3r^2)^4 = 81r^8
Example: In this case, we raise both the base number and the variable to the power of 4: 3^4 = 81 and (r^2)^4 = r^8.
These examples showcase how index laws can be applied to solve complex problems involving nested exponents and multiple variables.
Highlight: Mastering these complex manipulations is essential for success in higher-level mathematics courses.
The page also includes additional examples that further reinforce the application of various index laws in different scenarios.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Index Laws: Addition and Multiplication
The first page introduces two fundamental laws of indices: the addition law and the multiplication law. These laws are essential for simplifying expressions involving exponents.
Definition: Index laws are rules that govern how to manipulate expressions with exponents.
The page presents three key laws:
- Addition of powers: y^a × y^b = y^(a+b)
- Subtraction of powers: y^a ÷ y^b = y^(a-b)
- Multiplication of powers: (y^a)^b = y^(a×b)
Example: Using the addition law, we can simplify x^3 × x^4 to x^7 because 3 + 4 = 7.
These laws form the foundation for more complex operations with indices and are crucial for solving algebraic equations efficiently.
Highlight: The multiplication law of indices is particularly useful in simplifying nested exponents.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user