Simplify the expression (8x^3y^2/4a^2b^4) ^-2

A. 4x^6y^4/a^4b^8

B. a^4b^8/2x^6y^4

C. a^4b^8/4x^6y^4

D. a^4b^6/2x^5y^4

Simplify the following:

((8 x^3 y^2 a^2 b^4) / 4) ^ (-2)

8/4 = (4*2) / 4 = 2:

(2 x^3 y^2 a^2 b^4) ^ (-2)

Multiply each exponent in 2 x^3 y^2 a^2 b^4 by - 2:

(x^ (-2*3) y^ (-2*2) a^ (-2*2) b^ (-2*4)) / (2^2)

-2*3 = - 6:

(x^ (-6) y^ (-2*2) a^ (-2*2) b^ (-2*4)) / 2^2

-2*2 = - 4:

(y^ (-4) a^ (-2*2) b^ (-2*4)) / (2^2 x^6)

-2*2 = - 4:

(a^ (-4) b^ (-2*4)) / (2^2 x^6 y^4)

-2*4 = - 8:

b^ (-8) / (2^2 x^6 y^4 a^4)

2^2 = 4:

Answer: 1 / (4 x^6 y^4 a^4 b^8) thus the answer is A