Exponent rules

Objective

Apply the product, quotient, power, zero, and negative exponent rules.

What it means

Exponent rules let you combine powers of the same base: multiply powers by adding exponents, divide by subtracting exponents, raise a power to a power by multiplying exponents, and any nonzero base to the zero power equals 1.

Key terms

Product rule

x^a * x^b = x^(a+b)

Quotient rule

x^a / x^b = x^(a-b)

Power rule

(x^a)^b = x^(a*b)

Negative exponent

x^(-n) = 1/x^n

Rules to remember

• Only combine exponents when the bases match.
• Zero exponent: any nonzero base to the 0 power is 1.
• Negative exponent means reciprocal, not a negative number.

Step by step

1. 1Identify the operationMultiplying same base powers, dividing, or a power raised to a power.
2. 2Apply the matching ruleAdd, subtract, or multiply the exponents accordingly.
3. 3Clean up negativesRewrite negative exponents as positive-exponent fractions.