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

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

• A. Add the exponents
• B. Subtract the exponents
• C. Multiply the exponents
• D. Divide the exponents

Answer: (B)

When dividing expressions with the same base, you subtract the exponents. Think of a^m as multiplying the base by itself m times. Dividing by a^n cancels n of those factors, leaving m−n copies of the base. So a^m / a^n = a^(m−n). For example, 3^5 ÷ 3^2 equals 3^(5−2) = 3^3 = 27. If the top exponent is smaller, you get a negative exponent, which means the reciprocal: 2^3 ÷ 2^5 = 2^(3−5) = 2^−2 = 1/4. This subtraction rule comes from how exponents count repeated multiplication and how division removes factors.

When dividing expressions with the same base, you subtract the exponents. Think of a^m as multiplying the base by itself m times. Dividing by a^n cancels n of those factors, leaving m−n copies of the base. So a^m / a^n = a^(m−n).

For example, 3^5 ÷ 3^2 equals 3^(5−2) = 3^3 = 27. If the top exponent is smaller, you get a negative exponent, which means the reciprocal: 2^3 ÷ 2^5 = 2^(3−5) = 2^−2 = 1/4.

This subtraction rule comes from how exponents count repeated multiplication and how division removes factors.