Exponents & Roots

Exponents (Powers)

An exponent tells you how many times to multiply a base by itself.

2³ = 2 × 2 × 2 = 8

• Base: 2
• Exponent: 3
• Result: 8 (read as "2 to the power of 3" or "2 cubed")

Squares and Cubes

Squaring means to the power of 2:

• 5² = 5 × 5 = 25

Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100…

Cubing means to the power of 3:

• 3³ = 3 × 3 × 3 = 27

Square Roots

The square root (√) is the reverse of squaring:

• √25 = 5 (because 5² = 25)
• √144 = 12

Cube Roots

The cube root (∛) is the reverse of cubing:

• ∛8 = 2 (because 2³ = 8)
• ∛27 = 3

Key Rules of Exponents

Rule	Example
a⁰ = 1	7⁰ = 1
a¹ = a	5¹ = 5
aᵐ × aⁿ = aᵐ⁺ⁿ	2³ × 2⁴ = 2⁷
aᵐ ÷ aⁿ = aᵐ⁻ⁿ	3⁵ ÷ 3² = 3³
(aᵐ)ⁿ = aᵐⁿ	(2³)² = 2⁶