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Understanding Year 9 Laws of Indices with Examples - Easy PDF Guide

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Understanding Year 9 Laws of Indices with Examples - Easy PDF Guide
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This comprehensive guide explains the laws of indices for Year 9 students, covering essential rules and examples to enhance understanding of exponents in mathematics.

Key points:

  • Covers seven fundamental rules of indices
  • Provides clear examples for each rule
  • Offers guidance on applying multiple rules in complex problems
  • Suggests additional resources for further learning

12/10/2022

791

laws of Indices
Rule 1 - 2²x2² = 24 you acel the Indices for both
number
numbers and the large
stays the same.
subtract the Indices for
larg

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Laws of Indices Explained for Year 9 Students

The laws of indices explained for Year 9 students are fundamental mathematical concepts that are crucial for GCSE preparation. This guide covers the 8 laws of indices with clear explanations and examples, making it an invaluable resource for students seeking to understand these important rules.

Definition: Indices, also known as exponents or powers, are mathematical notations that indicate how many times a number is multiplied by itself.

  1. Rule 1: Multiplication with the Same Base When multiplying terms with the same base, add the exponents while keeping the base the same.

    Example: 2² × 2² = 2⁴

  2. Rule 2: Division with the Same Base When dividing terms with the same base, subtract the exponents while keeping the base the same.

    Example: 5⁵ ÷ 5² = 5³

  3. Rule 3: Multiplication with Different Bases When multiplying terms with different bases, multiply the bases and add the exponents for like terms.

    Example: 3a¹ × 2a² = 6a³

  4. Rule 4: Power of a Power When raising a power to another power, multiply the exponents.

    Example: (7⁰)² = 7¹⁰

  5. Rule 5: Negative Indices Negative indices create reciprocals, changing the number to a fraction and removing the negative sign.

    Example: a⁻² = 1/a²

  6. Rule 6: Fractional Indices For fractional indices, convert the denominator to a root and use the numerator as a power.

    Example: 9³/² = (√9)³ = 3³ = 27

  7. Rule 7: Combining Rules Complex problems may require the application of multiple rules in sequence.

    Example: 9⁵/² = (9²)⁵/² = 81⁵/² = (√81)⁵ = 9⁵ = 59049

Highlight: For additional help, students are encouraged to seek assistance from their teachers or utilize online resources such as Hegarty Maths for video explanations.

This comprehensive guide to indices for Year 9 maths provides a solid foundation for understanding and applying the laws of indices. By mastering these rules, students will be well-prepared for more advanced mathematical concepts in their GCSE studies.

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Understanding Year 9 Laws of Indices with Examples - Easy PDF Guide

user profile picture

study now

@study_orgetnothing

·

10 Followers

Follow

This comprehensive guide explains the laws of indices for Year 9 students, covering essential rules and examples to enhance understanding of exponents in mathematics.

Key points:

  • Covers seven fundamental rules of indices
  • Provides clear examples for each rule
  • Offers guidance on applying multiple rules in complex problems
  • Suggests additional resources for further learning

12/10/2022

791

 

8/9

 

Maths

37

laws of Indices
Rule 1 - 2²x2² = 24 you acel the Indices for both
number
numbers and the large
stays the same.
subtract the Indices for
larg

Laws of Indices Explained for Year 9 Students

The laws of indices explained for Year 9 students are fundamental mathematical concepts that are crucial for GCSE preparation. This guide covers the 8 laws of indices with clear explanations and examples, making it an invaluable resource for students seeking to understand these important rules.

Definition: Indices, also known as exponents or powers, are mathematical notations that indicate how many times a number is multiplied by itself.

  1. Rule 1: Multiplication with the Same Base When multiplying terms with the same base, add the exponents while keeping the base the same.

    Example: 2² × 2² = 2⁴

  2. Rule 2: Division with the Same Base When dividing terms with the same base, subtract the exponents while keeping the base the same.

    Example: 5⁵ ÷ 5² = 5³

  3. Rule 3: Multiplication with Different Bases When multiplying terms with different bases, multiply the bases and add the exponents for like terms.

    Example: 3a¹ × 2a² = 6a³

  4. Rule 4: Power of a Power When raising a power to another power, multiply the exponents.

    Example: (7⁰)² = 7¹⁰

  5. Rule 5: Negative Indices Negative indices create reciprocals, changing the number to a fraction and removing the negative sign.

    Example: a⁻² = 1/a²

  6. Rule 6: Fractional Indices For fractional indices, convert the denominator to a root and use the numerator as a power.

    Example: 9³/² = (√9)³ = 3³ = 27

  7. Rule 7: Combining Rules Complex problems may require the application of multiple rules in sequence.

    Example: 9⁵/² = (9²)⁵/² = 81⁵/² = (√81)⁵ = 9⁵ = 59049

Highlight: For additional help, students are encouraged to seek assistance from their teachers or utilize online resources such as Hegarty Maths for video explanations.

This comprehensive guide to indices for Year 9 maths provides a solid foundation for understanding and applying the laws of indices. By mastering these rules, students will be well-prepared for more advanced mathematical concepts in their GCSE studies.

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the #1 education app in five European countries

4.9+

Average app rating

13 M

Pupils love Knowunity

#1

In education app charts in 12 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.