How do you simplify (x ^ { - 4} y ^ { - 2} \cdot x ^ { 2} y ^ { - 4} ) ^ { 2}(x−4y−2⋅x2y−4)2?

1 Answer
Aswin K.
Aug 11, 2017

x^-4*y^-12x−4⋅y−12

Explanation:

(x^-4y^-2*x^2y^-4)^2(x−4y−2⋅x2y−4)2

=>(x^-4y^-2*x^2y^-4)^2⇒(x−4y−2⋅x2y−4)2

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

=>(x^-4*x^2*y^-2*y^-4)^2⇒(x−4⋅x2⋅y−2⋅y−4)2

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

=>(x^-2*y^(-2-4))^2⇒(x−2⋅y−2−4)2

=>(x^-2*y^-6)^2⇒(x−2⋅y−6)2

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

=>x^(-2*2)*y^(-6*2)⇒x−2⋅2⋅y−6⋅2

=>x^-4*y^-12⇒x−4⋅y−12

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