How do you simplify #[(xy^6)/(x^3y)]^-2#?

1 Answer
Mar 25, 2018

Answer:

#=> x^4/y^10#

Explanation:

We start with:

#=>[(xy^6)/(x^3y)]^-2#

We multiply all powers by #-2#:

#=>(x^(-2)y^(6(-2)))/(x^(3(-2))y^(-2))#

Simplifying powers:

#=>(x^-2 y^-12)/(x^-6 y ^-2)#

Division of terms with powers requires subtraction of powers:

#=> x^(-2 - (-6)) y^(-12 - (-2))#

Simplifying:

#=>x^4y^-10#

We can get rid of negative powers by moving #y# to the denominator:

#=> x^4/y^10#