Indices (also called powers or exponents) are mathematical shortcuts that... Show more
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Basic Index Rules You Need to Know
Learning index rules is like having a calculator built into your brain – they make tricky maths problems surprisingly simple! When you multiply numbers with the same base, you just add the powers together. For example, x² × x⁶ = x⁸ because 2 + 6 = 8.
Division works the opposite way – you subtract the powers instead. So y² ÷ y³ = y⁻¹ because 2 - 3 = -1. This might give you a negative power, but don't worry – that's perfectly normal!
Here's a handy fact: anything to the power of 0 equals 1. So m⁰ = 1, no matter what m is (as long as it's not zero). When you see brackets with powers inside and outside, like (k⁴)³, you multiply them together: 4 × 3 = 12, so the answer is k¹².
Quick Tip: Remember "MADSPM" – Multiply Add, Divide Subtract, Power Multiply!
Negative and Fractional Powers Made Simple
Negative powers aren't scary once you know the secret – they just mean "flip it and make it positive." So 3⁻² = 1/3² = 1/9. Think of the negative sign as instructions to put the number on the bottom of a fraction instead.
Fractional powers are actually roots in disguise. When you see 25^(1/2), the bottom number (2) tells you it's a square root, so the answer is 5. For something like 9^(3/2), you take the square root first (getting 3), then cube it (getting 27).
The trickiest bit is combining negative and fractional powers, like 16^(-3/2). First work out 16^(3/2): take the square root (4), then cube it (64). Because of the negative sign, your final answer is 1/64.
When dealing with fractions like (4/9)^(3/2), apply the power to both the top and bottom separately. Square root of 4 is 2, cubed gives 8. Square root of 9 is 3, cubed gives 27. So your answer is 8/27.
Remember: With negative fractional powers of fractions, work out the positive version first, then flip your final answer!
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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.
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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.
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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.
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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
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THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. 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 Knowunity AI. 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
Understanding Indices: Examples and Practice
Indices (also called powers or exponents) are mathematical shortcuts that make calculations with repeated multiplication much easier. Once you master the basic rules, you'll find yourself solving complex-looking problems in seconds rather than minutes.
Basic Index Rules You Need to Know
Learning index rules is like having a calculator built into your brain – they make tricky maths problems surprisingly simple! When you multiply numbers with the same base, you just add the powers together. For example, x² × x⁶ = x⁸ because 2 + 6 = 8.
Division works the opposite way – you subtract the powers instead. So y² ÷ y³ = y⁻¹ because 2 - 3 = -1. This might give you a negative power, but don't worry – that's perfectly normal!
Here's a handy fact: anything to the power of 0 equals 1. So m⁰ = 1, no matter what m is (as long as it's not zero). When you see brackets with powers inside and outside, like (k⁴)³, you multiply them together: 4 × 3 = 12, so the answer is k¹².
Quick Tip: Remember "MADSPM" – Multiply Add, Divide Subtract, Power Multiply!
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Negative and Fractional Powers Made Simple
Negative powers aren't scary once you know the secret – they just mean "flip it and make it positive." So 3⁻² = 1/3² = 1/9. Think of the negative sign as instructions to put the number on the bottom of a fraction instead.
Fractional powers are actually roots in disguise. When you see 25^(1/2), the bottom number (2) tells you it's a square root, so the answer is 5. For something like 9^(3/2), you take the square root first (getting 3), then cube it (getting 27).
The trickiest bit is combining negative and fractional powers, like 16^(-3/2). First work out 16^(3/2): take the square root (4), then cube it (64). Because of the negative sign, your final answer is 1/64.
When dealing with fractions like (4/9)^(3/2), apply the power to both the top and bottom separately. Square root of 4 is 2, cubed gives 8. Square root of 9 is 3, cubed gives 27. So your answer is 8/27.
Remember: With negative fractional powers of fractions, work out the positive version first, then flip your final answer!
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?
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4.6/5
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4.7/5
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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
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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 Knowunity AI. 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
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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
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Elisha
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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
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