When multiplying two powers with the same base, what do you do to the exponents?

When multiplying two powers with the same base, what do you do to the exponents?

• A. Subtracting exponents
• B. Adding exponents
• C. Multiplying exponents
• D. Dividing exponents

Answer: (B)

When you multiply two powers with the same base, you add the exponents. Think of each exponent as counting how many times you multiply the base by itself, and combining two such counts means you’ve got that many more copies. So a^m times a^n is a^(m+n). For example, 3^4 * 3^2 = 3^(4+2) = 3^6. This works because the base is the same, so you’re effectively multiplying together a total of m + n copies of that base. For contrast, dividing would subtract the exponents (a^m / a^n = a^(m-n)), and raising a power to another power uses multiplication of exponents ((a^m)^k = a^(m k)).

When you multiply two powers with the same base, you add the exponents. Think of each exponent as counting how many times you multiply the base by itself, and combining two such counts means you’ve got that many more copies. So a^m times a^n is a^(m+n). For example, 3^4 * 3^2 = 3^(4+2) = 3^6.

This works because the base is the same, so you’re effectively multiplying together a total of m + n copies of that base. For contrast, dividing would subtract the exponents (a^m / a^n = a^(m-n)), and raising a power to another power uses multiplication of exponents ((a^m)^k = a^(m k)).