Question

Simplify x^2×(x^3÷x^-2/x^2÷x^-3)​

Answer 1

x^8

Explanation:

Simplify the following:

(x^2 x^3)/(x^(-2) x^2 x^(-3))

Multiply the numerator of (x^3)/((x^2)/(x^2) x^(-3)) by the reciprocal of the denominator. (x^3)/((x^2)/(x^2) x^(-3)) = (x^3 x^3)/((x^2)/(x^2)):

x^2 (x^3 x^3)/((x^2)/(x^2))

(x^3 x^3 x^2)/((x^2)/(x^2)) = x^2/x^2×(x^3 x^3)/x^(-2) = (x^3 x^3)/x^(-2):

(x^3 x^3)/x^(-2)

Combine powers. (x^3 x^3)/x^(-2) = x^(3 + 3 + 2):

x^(3 + 3 + 2)

3 + 3 + 2 = 8:

Answer: x^8