Study Notes
Exponents are a way to represent repeated multiplication of the same number. They simplify expressions and calculations.
- Exponent — a number that indicates how many times the base is multiplied by itself. Example: 4^3 = 4 x 4 x 4
- Product of Powers Rule — when multiplying like bases, add the exponents. Example: a^m x a^n = a^(m+n)
- Quotient of Powers Rule — when dividing like bases, subtract the exponents. Example: a^m ÷ a^n = a^(m-n)
- Power of a Power Rule — when raising a power to another power, multiply the exponents. Example: (a^m)^n = a^(m*n)
- Negative Exponent Rule — a negative exponent means the reciprocal of the base raised to the opposite positive exponent. Example: a^-m = 1/a^m
- Fractional Exponent Rule — a fractional exponent represents a root. Example: a^(1/m) = m√a
- Zero Exponent Rule — any non-zero base raised to the power of zero is 1. Example: a^0 = 1
Exam Tips
Key Definitions to Remember
- Exponent: a number indicating repeated multiplication
- Base: the number being multiplied
- Power: the result of raising a base to an exponent
Common Confusions
- Confusing negative exponents with negative numbers
- Misapplying the power of a power rule
Typical Exam Questions
- Simplify (2n)^4 ÷ 8n^6? Answer: 1/n^2
- Evaluate 9^0? Answer: 1
- Solve (4^-1 + 8^-1) ÷ (2/3)^-1? Answer: 1/4
What Examiners Usually Test
- Understanding and applying exponent rules
- Simplifying expressions with exponents
- Solving equations involving exponents