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

• Show Step-by-Step Solutions

• Printable & Online Exponent Worksheets

  Printable
  Product Rule
  Quotient Rule
  Power Rule
  Negative Exponents
  Fractional exponents
  Laws of Exponents
  

  Online
  Apply Law of Exponents (multiply)
  Apply Law of Exponents (mixed)

Free Exponent Games Online
Multiply Exponents	Divide Exponents	Power of a Power
Power of a Product	Negative Exponents	Fractional Exponents

 

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.

• Show Step-by-Step Solutions

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

• Show Step-by-Step Solutions

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.

• Show Step-by-Step Solutions

Indices beastie - Dare you try this difficult question

• Show Step-by-Step Solutions

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

• Show Step-by-Step Solutions

Check out our most popular games!

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.