Exponent Rules and Properties

Exponents are a shorthand for repeated multiplication: a^n = underbrace{a cdot a cdot a cdots a}_{n text{ times}}. Here are the seven essential rules you need for the SAT: | Rule | Formula | Example | |---|---|---| | Product Rule | a^m cdot a^n = a^{m+n} | x^3 cdot x^4 = x^7 | | Quotient Rule | frac{a^m}{a^n} = a^{m-n} | frac{x^5}{x^2} = x^3 | | Power Rule | (a^m)^n = a^{mn} | (x^3)^2 = x^6 | |…

The SAT loves to combine multiple rules in one problem. The key: work step by step and apply one rule at a time.

Example: Simplify frac{x^5 cdot x^3}{x^2}