which expression is equivalent to (-4x^3 y^-5)^2
A) 16y^10/x^10
B)-8y^7/x^5
C)16xx^6 y^-10
D)16y^10/x^6
E)-8x^-5 y^7
To find the equivalent expression, we need to square both the -4 and the x^3 y^-5 within the parentheses.
(-4x^3 y^-5)^2 = (-4)^2 * (x^3)^2 * (y^-5)^2
Simplifying each term:
(-4)^2 = 16
(x^3)^2 = x^(3*2) = x^6
(y^-5)^2 = y^(-5*2) = y^-10
Putting it all together:
(-4x^3 y^-5)^2 = 16 * x^6 * y^-10
Since y^-10 is the same as 1/y^10, the expression becomes:
16x^6 * 1/y^10 = 16x^6/y^10
Therefore, the correct answer is:
C) 16x^6 y^-10