Simplify the expression. (3x/y) ^-3

a. 27x^3 y^3

b. 27/x^3y^3

c. y^3/27x^3

d. 27x^3/y^3

y^3 / (27 x^3)

Step-by-step explanation:

Simplify the following:

((3 x) / y) ^ (-3)

((3 x) / y) ^ (-3) = (y / (3 x)) ^3:

(y / (3 x)) ^3

Multiply each exponent in y / (3 x) by 3:

(y^3) / ((3 x) ^3)

Multiply each exponent in 3 x by 3:

y^3 / (3^3 x^3)

3^3 = 3*3^2:

y^3 / (3*3^2 x^3)

3^2 = 9:

y^3 / (3*9 x^3)

3*9 = 27:

Answer: y^3 / (27 x^3)