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More Lessons for GCSE Maths

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Videos, examples, and solutions to help GCSE Maths students learn about indices by working through some examination questions.

**All you need to know about indices (Revision and Summary)**

x^{1} means x multiplied repeatedly by itself n times.

x^{m}x^{n} = x^{m + n}

(x^{m})^{n} = x^{mn}

(x^{m}y^{n})^{p} = x^{mp}y^{np}

x^{m}/x^{n} = x^{m-n}

x^{0} = 1

x^{-n} = 1/x^{n}

**Indices GCSE Maths revision Higher level worked exam questions (include fractional and negative powers)**

Examples:

1. Work out 56^{1} - 56^{0}

2. Explain why 27^{1/3} = 3

3. Write 27^{-1/3} as a fraction.

4. Work out the value of 64^{2/3}

5. Work out all solutions of the equation: 8^{m} = 2^{m2}

6. Show clearly that 4^{3/2} = 8

. Hence, or otherwise, work out the value of y if 4^{y} = 8^{6}

7. Write down the value of 2^{0}.

8. Simplify 7^{18} ÷ (7^{3})^{2}. Give your answer as a power of 7.

9. A patient has a disease. She has 4^{3} body cells on day 1. The number of affected cells doubles every day. The disease becomes serious when 2^{10} body cells are affected. On which day does the disease become serious? You must show your working.

10. Work out 10^{-2} × 64^{1/2}.

11. Write down the square of the cube root of x using index notation.

12. Given x = 8, what is the value of the square of the cube root of x?

13. Work out the value of 9^{-3/2}.

14. Evaluate 27^{-2/3}.

15. Explain why 25^{4} = 5^{8}.

16. Write 4^{-1} as a fraction.

17. Work out 8^{4/3}.
**Indices (Exponents) : C1 Edexcel June 2013 Q3**

(a) Find the value 8^{5/3}

(b) Simplify fully (2x^{1/2})^{3}/(4x^{2})

**Indices Tricky - GCSE Further Maths revision Exam paper practice & help**

Example:

x^{3/2} = 8 where x > 0 and y^{-2} = 25/4 where y > 0.

Work out the value of x/y.

**Indices beastie - Dare you try this difficult question**

**Indices and Surds - GCSE Maths Higher revision Exam paper practice & help**

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for GCSE Maths

Math Worksheets

Videos, examples, and solutions to help GCSE Maths students learn about indices by working through some examination questions.

x

x

(x

(x

x

x

x

Examples:

1. Work out 56

2. Explain why 27

3. Write 27

4. Work out the value of 64

5. Work out all solutions of the equation: 8

6. Show clearly that 4

. Hence, or otherwise, work out the value of y if 4

7. Write down the value of 2

8. Simplify 7

9. A patient has a disease. She has 4

10. Work out 10

11. Write down the square of the cube root of x using index notation.

12. Given x = 8, what is the value of the square of the cube root of x?

13. Work out the value of 9

14. Evaluate 27

15. Explain why 25

16. Write 4

17. Work out 8

(a) Find the value 8

(b) Simplify fully (2x

Example:

x

Work out the value of x/y.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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