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