Year 9: Evaluate expressions involving exponents

This cheat sheet will help you understand and evaluate expressions that use exponents (also known as 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 = Base^{(Number of times to multiply)} - This is the fundamental rule.
• Any non-zero number raised to the power of 0 equals 1 (e.g., 5⁰ = 1).
• Negative Exponents: A negative exponent means the reciprocal of the base raised to the positive exponent. For example, 2^-2 = 1/2² = 1/4.
• Fractional Exponents: A fractional exponent is the square root or nth root of the base. For example, 9^1/2 = √9 = 3.

Examples

• 2³ = 8
• 3² = 9
• 5^-2 = 1/25
• 4^1/2 = √4 = 2

Remember to follow the order of operations (BODMAS/PEMDAS) when evaluating expressions with exponents. Exponents are usually performed *after* addition, subtraction, multiplication and division.