When you raise a power to another power, how do you combine the exponents?

• A. Add exponents
• B. Keep same exponent
• C. Multiply exponents
• D. Divide exponents

Answer: (C)

Raising a power to another power multiplies the exponents. For any base a and integers m and n, (a^m)^n = a^(m n). Think of a^m as a multiplied by itself m times. When you raise that to the power n, you repeat that entire block n times, giving a appearing a total of m × n times. For example, (3^2)^4 = 3^(2×4) = 3^8. This shows why the exponents multiply. If you were dealing with multiplying two powers with the same base, you’d add the exponents, but nesting a power inside another power yields multiplication of the exponents.