How do you simplify #(\frac { x ^ { - 4} y ^ { 2} } { x ^ { 5} y ^ { 6} } ) ^ { 2}#?

1 Answer
Mar 30, 2017

#(1/(x^18y^8))#

Explanation:

The first thing we should do is multiply each exponent by #2#

#((x^-4y^2)/(x^5y^6))^2 -> ((x^(-4*2)y^(2*2))/(x^(5*2)y^(6*2))) -> ((x^-8y^4)/(x^10y^12))#

What we could do next is rewrite the expression using only positive exponents. You'll notice that #x^-8# is a negative exponent so we have to make positive using this rule: #(a^(-b)=1/a^b)# Basically, we are moving the #x^-8# to the denominator.

This would result in:

#((y^4)/(x^8x^10y^12))#

Finally, we can simply the expression using the following rules:

#x^a*x^b=x^(a+b)#

#x^a/x^b=x^(a-b)#

Thus:

#((y^4)/(x^8x^10y^12)) : x^8*x^10 = x^(8+10) = x^18; y^4/y^12 = 1/(y^8)#

So our final answer is...

#(1/(x^18y^8))#