(a^n)^m equals which expression?

(a^n)^m equals which expression?

• A. a^(n+m)
• B. a^(n/m)
• C. a^(nm)
• D. (a^n)^m

Answer: (C)

When you raise a power to another power, you multiply the exponents. So (a^n)^m simplifies to a^(n·m), because you're applying the exponent m to the exponent n. That means the expression equals a^(nm). The other forms don’t match the rule: a^(n+m) would come from multiplying two bases with the same base, not from raising a power to another power; a^(n/m) would come from dividing exponents, which isn’t what this operation does. The original written form is a restatement of the operation, but a^(nm) is the standard simplified form.

When you raise a power to another power, you multiply the exponents. So (a^n)^m simplifies to a^(n·m), because you're applying the exponent m to the exponent n.

That means the expression equals a^(nm). The other forms don’t match the rule: a^(n+m) would come from multiplying two bases with the same base, not from raising a power to another power; a^(n/m) would come from dividing exponents, which isn’t what this operation does. The original written form is a restatement of the operation, but a^(nm) is the standard simplified form.