How do you simplify #((2x^-5y^2) / (4x^3y^-4)) ^-3#?

1 Answer
Nov 24, 2015

Answer:

#8 x^24 y^(-18)#

Explanation:

Let's remember the power rules first:

#a^m * a^n = a^(m+n)#

#a^(-m) = 1/ a^m #

#(a^m)^n = a*(m*n)#

#(a * b)^m = a^m * b^m #

Now, let's use these rules to simplify your expression:

#((2x^(-5) y^2)/(4x^3 y^(-4)))^(-3) = (2/4 * x^(-5)/x^3 * y^2 / y^(-4))^(-3)#

#color(white)(xxxxxxxxxx) = (1/2 * x^(-5) * x^(-3) * y^2 * y^4)^(-3)#

#color(white)(xxxxxxxxxx) = (1/2 * x^(-8) * y^6)^(-3)#

#color(white)(xxxxxxxxxx) = (1/2)^(-3) * (x^(-8))^(-3) * (y^6)^(-3)#

#color(white)(xxxxxxxxxx) = 2^3 * x^24 * y^(-18)#

#color(white)(xxxxxxxxxx) = 8 x^24 y^(-18)#

#color(white)(xxxxxxxxxx) = (8 x^24) / y^18#

Hope that this helped!