Power of a Power

When a quantity already written as a power is raised to another power, you are repeating multiplication of the same base inside the brackets. That means the same factor appears m times for each of the n groups, so the total number of factors is m × n. This is why you keep the base and multiply the exponents: (a^m)^n = a^(mn).

Use this rule when simplifying expressions that contain a power inside parentheses, especially in algebra, scientific notation, and index laws. It also helps when working with variables or numbers in exponent form and you want to rewrite the expression with a single exponent.

• adding the exponents instead of multiplying them
• changing the base instead of keeping the same base
• forgetting that the outer exponent applies to every factor inside the parentheses