If you raise a product (ab) to a power n, how should the exponent be applied?

• A. To both a and b
• B. Only to a
• C. To neither
• D. To the product as a whole

Answer: (A)

Raising a product to a power means the exponent applies to each factor inside the parentheses. Writing (ab) raised to the n-th power as (ab)^n means you multiply the whole product by itself n times: (ab)(ab)...(ab) with n copies. In that process, the a’s multiply together n times to give a^n and the b’s multiply together n times to give b^n. Because multiplication is associative and commutative, you can regroup to get a^n b^n. This is the clear way to see why the exponent affects both parts of the product. The same result comes from applying the exponent to each factor inside, which aligns with the standard rule (ab)^n = a^n b^n.