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

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Answer 1 · 2018-03-25T20:56:44

#=> x^4/y^10#

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#