Question

To divide x³y by x⁴y, first divide y by y to get x³/x⁴. Which of these would you do next to solve?

A: x(³-⁴)
B: x(³/⁴)
C: x(⁴-³)
D: x(⁴/³)

Answer 1

To divide x³y by x´y, we simplify by subtracting the exponents, resulting in x^(3-4)=x^(-1), which means that the correct answer is A: x(3-4).

Step-by-step explanation:

To solve the division of x³y by x´y, you need to divide the variables separately. When dividing variables with exponents, you subtract the exponent of the denominator from the exponent of the numerator. Thus, after canceling out the variable y since y/y = 1, we are left with x³/x´, which simplifies by using the rule

• x^n / x^m = x^(n-m)

Therefore, the correct operation to perform next would be x³/x´ = x^(3-4) = x^(-1). This means that x^(-1) is in fact equal to 1/x, according to the property that a negative exponent denotes a reciprocal.

As such, the answer to the student's question is A: x³/x´ = x^(3-4) = x^(-1), and this represents division of exponentials using subtraction of exponents.