Exam Questions On Indices

All You Need To Know About Indices (Revision and Summary)

xⁿ means x multiplied repeatedly by itself n times.
x^mxⁿ = x^{m + n}
(x^m)ⁿ = x^mn
(x^myⁿ)^p = x^mpy^np
x^m/xⁿ = x^m-n
x⁰ = 1
x^-n = 1/xⁿ

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Indices GCSE Maths Revision Higher Level Worked Exam Questions (include fractional and negative powers)

Examples:

1. Work out 56¹ - 56⁰
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 = 8⁶
7. Write down the value of 2⁰.
8. Simplify 7¹⁸ ÷ (7³)². Give your answer as a power of 7.
9. A patient has a disease. She has 4³ body cells on day 1. The number of affected cells doubles every day. The disease becomes serious when 2¹⁰ 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 25⁴ = 5⁸.
16. Write 4^-1 as a fraction.
17. Work out 8^4/3.

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Indices (Exponents) : C1 Edexcel June 2013 Q3
(a) Find the value 8^5/3
(b) Simplify fully (2x^1/2)³/(4x²)

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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.

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Indices beastie - Dare you try this difficult question

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

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