When dividing two powers with the same base, what operation is performed on the exponents?

When dividing two powers with the same base, what operation is performed on the exponents?

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

Answer: (D)

Subtracting the exponents is what happens when you divide powers with the same base. In general, a^m divided by a^n equals a^(m−n) as long as the base a is nonzero. The idea is that dividing by a^n removes n factors of the base from a^m, leaving m−n factors. For example, 3^7 ÷ 3^4 equals 3^(7−4) = 3^3 = 27. This rule works for integers and, with nonzero bases, also when exponents are negative: 2^5 ÷ 2^7 = 2^(5−7) = 2^(-2).

Subtracting the exponents is what happens when you divide powers with the same base. In general, a^m divided by a^n equals a^(m−n) as long as the base a is nonzero. The idea is that dividing by a^n removes n factors of the base from a^m, leaving m−n factors. For example, 3^7 ÷ 3^4 equals 3^(7−4) = 3^3 = 27. This rule works for integers and, with nonzero bases, also when exponents are negative: 2^5 ÷ 2^7 = 2^(5−7) = 2^(-2).