How do you simplify (x ^ { - 4} y ^ { - 2} \cdot x ^ { 2} y ^ { - 4} ) ^ { 2}?

1 Answer
Aug 11, 2017

x^-4*y^-12

Explanation:

(x^-4y^-2*x^2y^-4)^2

=>(x^-4y^-2*x^2y^-4)^2

a^n*a^m=a^(n+m),multiplying as per this equation within the brackets.

=>(x^-4*x^2*y^-2*y^-4)^2

=>(x^(-4+2)*y^(-2+ -4))^2

=>(x^-2*y^(-2-4))^2

=>(x^-2*y^-6)^2

(x^n)^m=x^(n*m),so (x^n*y^p)^m=x^(n*m)*y^(p*m), from this we can simply the equation as:

=>x^(-2*2)*y^(-6*2)

=>x^-4*y^-12