Know and apply the properties of integer exponents

What you'll learn

1. State and apply the product of powers rule (a^m * a^n = a^(m+n)) and the quotient of powers rule (a^m / a^n = a^(m-n)) to simplify expressions with the same base
2. Apply the power of a power rule ((a^m)^n = a^(mn)), the power of a product rule ((ab)^n = a^n * b^n), and the power of a quotient rule ((a/b)^n = a^n / b^n) to rewrite expressions in equivalent forms
3. Explain why a^0 = 1 for any nonzero base a by extending the pattern of decreasing exponents, and apply this definition to simplify expressions
4. Explain why a^(-n) = 1/a^n for any nonzero base a by extending the same pattern, and convert expressions with negative exponents into equivalent expressions with positive exponents
5. Combine multiple exponent properties in a single expression to generate equivalent numerical expressions, including expressions that require two or more rules applied in sequence