Which expression is equivalent to (−4x^−3 y^−5)^2

Question

Select all that apply.

(2 points)
Responses

negative 8 x to the negative 5 power y to the 7th power

16 x to the negative 6 power y to the negative 10 power

the fraction with numerator 16 y to the 10th power and denominator x to the 10th power

the fraction with numerator negative 8 y to the 7th power and denominator x to the 5th power

sixteen y to the negative tenth power with a denominator of x to the sixth

Answer 1

To simplify the expression (−4x^−3 y^−5)^2, we can square both the coefficient and the variables inside the parentheses.

(-4)^2 = 16

(x^−3)^2 = x^(-3 * 2) = x^(-6) = 1/x^6

(y^−5)^2 = y^(-5 * 2) = y^(-10) = 1/y^10

So, squaring the given expression gives us:

(−4x^−3 y^−5)^2 = 16 * (1/x^6) * (1/y^10)

Simplifying further, we get:

16 * (1/x^6) * (1/y^10) = 16/y^10x^6

Therefore, the equivalent expression is:

the fraction with numerator 16 and denominator y^10x^6