# Exam Questions On Indices

These lessons help GCSE/IGCSE Maths students learn about indices by working through some examination questions.

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

xn means x multiplied repeatedly by itself n times.
xmxn = xm + n
(xm)n = xmn
(xmyn)p = xmpynp
xm/xn = xm-n
x0 = 1
x-n = 1/xn

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

Examples:

1. Work out 561 - 560
2. Explain why 271/3 = 3
3. Write 27-1/3 as a fraction.
4. Work out the value of 642/3
5. Work out all solutions of the equation: 8m = 2m2
6. Show clearly that 43/2 = 8
. Hence, or otherwise, work out the value of y if 4y = 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 × 641/2.
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 84/3.

Indices (Exponents) : C1 Edexcel June 2013 Q3
(a) Find the value 85/3
(b) Simplify fully (2x1/2)3/(4x2)

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

Example:
x3/2 = 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

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