Year 8: Evaluate expressions involving exponents

This cheat-sheet will help you understand and solve problems involving exponents (also called powers).

What are Exponents?

An exponent tells you how many times to multiply a number by itself. For example, 2³ means 2 multiplied by itself 3 times: 2 x 2 x 2 = 8.

Key Rules

• Base x Base = Base²: For example, 3² = 3 x 3 = 9
• Baseⁿ x Base^m = Base^n+m: You can add exponents when multiplying expressions with the same base. For example, 2² x 2³ = 2²⁺³ = 2⁵ = 32
• Baseⁿ / Base^m = Base^n-m: You can subtract exponents when dividing expressions with the same base. For example, 8⁴ / 8² = 8^4-2 = 8² = 64
• (Baseⁿ)^m = Base^{n x m}: When raising a power to another power, multiply the exponents. For example, (2³)² = 2^{(3 x 2)} = 2⁶ = 64

Examples

Evaluate:

• 3⁴ = 3 x 3 x 3 x 3 = 81
• 5² x 5³ = 5⁽²⁺³⁾ = 5⁵ = 3125
• 10⁴ / 10² = 10^(4-2) = 10² = 100

Remember to always simplify your answers.