When multiplying expressions with the same base, what do you do with the exponents?

When multiplying expressions with the same base, what do you do with the exponents?

• A. Add the exponents
• B. Subtract the exponents
• C. Multiply the bases
• D. Keep exponents unchanged

Answer: (A)

When multiplying expressions with the same base, you add the exponents. Think of a^m as the base multiplied by itself m times; multiplying by a^n adds n more copies, giving a^(m+n). For example, 3^4 * 3^2 equals 3^(4+2) = 3^6, which is 729. This works for any nonzero base. Subtracting exponents would apply to division, keeping exponents unchanged ignores the extra factors, and changing the base would alter the base itself rather than combining the exponents.

When multiplying expressions with the same base, you add the exponents. Think of a^m as the base multiplied by itself m times; multiplying by a^n adds n more copies, giving a^(m+n). For example, 3^4 * 3^2 equals 3^(4+2) = 3^6, which is 729. This works for any nonzero base. Subtracting exponents would apply to division, keeping exponents unchanged ignores the extra factors, and changing the base would alter the base itself rather than combining the exponents.