Exponents & Powers • Topic 1 of 2

Writing Repeated Multiplication as Exponents

An exponent tells how many times to multiply a number (the base) by itself.

5 x 5 x 5 = 5^3 (read as '5 to the power of 3' or '5 cubed')

Term	Meaning	Example
Base	The number being multiplied	5
Exponent	How many times to multiply	3
Power	The whole expression	5^3 = 125

Special cases:

a^1 = a (any number to power 1 is itself)
a^0 = 1 (any nonzero number to power 0 is 1)
1^n = 1 (one raised to any power is 1)

EXPONENTIAL GROWTH:
  2^1 = 2    **
  2^2 = 4    ****
  2^3 = 8    ********
  2^4 = 16   ****************

LAWS OF EXPONENTS:
  Same base, multiply: a^m x a^n = a^(m+n)
  Same base, divide:   a^m / a^n = a^(m-n)
  Power of power:      (a^m)^n   = a^(m*n)

Solved Examples

Worked Example

Write 7 x 7 x 7 x 7 using exponents.

Solution7^4 (four 7's multiplied together)

Worked Example

Write 10^5 as repeated multiplication.

Solution10 x 10 x 10 x 10 x 10 = 100,000

Worked Example

Evaluate 2^6.

Solution2 x 2 x 2 x 2 x 2 x 2 = 64

Key Points

Exponent = how many times the base is multiplied by itself
Any nonzero number to power 0 = 1
a^m x a^n = a^(m+n) when bases are the same
(a^m)^n = a^(m*n)

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.$2\times2\times2=$

Explanation: Three $2$s $=2^3$.

Q2.In $5^3$, the number $5$ is the:

Explanation: The base.

Q3.$2^4=$

Explanation: $2\times2\times2\times2$.

Q4.$10^2=$

Explanation: $10\times10$.

Practice more MCQs → 📝 Assignment · 35 marks