Power Of A Product: Which identity is correct for (ab)^m?

Power Of A Product: Which identity is correct for (ab)^m?

• A. (ab)^m = a^m b^m
• B. (ab)^m = a^m + b^m
• C. (ab)^m = a^m - b^m
• D. (ab)^m = a^m b^n

Answer: (A)

Raising a product to a power applies the exponent to each factor in the product. So (ab)^m means you multiply a by itself m times and b by itself m times, then multiply those results: a^m b^m. This happens because the exponent distributes over multiplication, not over addition or subtraction. The other forms would mix or omit applying the exponent to both factors, which isn’t how the rule works.

Raising a product to a power applies the exponent to each factor in the product. So (ab)^m means you multiply a by itself m times and b by itself m times, then multiply those results: a^m b^m. This happens because the exponent distributes over multiplication, not over addition or subtraction. The other forms would mix or omit applying the exponent to both factors, which isn’t how the rule works.