By Chrystal Doucette • Updated August 30, 2022
Exponents (or powers) compress repeated multiplication into a single symbol. The base is the number being multiplied, and the exponent indicates how many times the base appears in the product. Understanding how to apply the rules for positive and negative bases—and how parentheses affect the result—is essential for accurate calculations.
Determine whether the base is positive or negative.
Parentheses change the meaning of a negative base. For instance, (-3)^4 differs from -3^4.
With a positive base, simply multiply the base by itself the number of times indicated by the exponent. Example: 5^3 = 5 × 5 × 5 = 125.
When the negative sign is inside parentheses, keep it with each factor. Example: (-3)^4 = (-3) × (-3) × (-3) × (-3) = 81.
If the negative sign is outside the parentheses, apply it only after all multiplications are done. Example: -3^4 = -(3 × 3 × 3 × 3) = -81.
When two exponents share the same base, add the exponents: 2^3 × 2^4 = 2^(3+4) = 2^7 = 128. This rule simplifies complex expressions before evaluation.
Always handle expressions inside parentheses first—this applies to both positive and negative bases.
