Study Notes
Exponents, also known as indices, are used to represent repeated multiplication of the same number or variable. They simplify expressions and calculations.
- Exponent — a number that indicates how many times a 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^(mn)
- Negative Exponent Rule — a negative exponent indicates 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; the denominator is the root and the numerator is the power. Example: a^(1/m) = m√a
Exam Tips
Key Definitions to Remember
- Exponent: a number indicating repeated multiplication
- Base: the number being multiplied
- Negative exponent: reciprocal of the base raised to the positive exponent
Common Confusions
- Confusing negative exponents with negative numbers
- Forgetting to apply the power of a power rule correctly
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 the rules of exponents
- Simplifying expressions using exponent rules
- Evaluating expressions with zero and negative exponents