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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.

**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**

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.

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