Using the quotient rule, simplify x^5 / x^2.

• A. x^3
• B. x^7
• C. x^2
• D. x^5

Answer: (A)

Dividing powers with the same base uses subtracting exponents. Here, you have x^5 divided by x^2, so you subtract the exponents: 5 - 2 = 3. The result is x^3. This works for all nonzero x, since the original fraction would be undefined at x = 0. The idea you’re using is that sharing the same base lets you combine the powers by subtracting their exponents, not by keeping the numerator’s exponent or adding them.