How do you simplify #(4x y ^ { - 2} ) ^ { - 3}#?

1 Answer
Jim G.
Oct 24, 2016

#(y^6)/(64x^3)#

Explanation:

Using #color(blue)"laws of exponents"#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)((a^mb^p)^n=a^(mn)b^(pn))color(white)(2/2)|)))#

#rArr(4xy^-2)^-3=4^(1xx-3)x^(1xx-3)y^(-2xx-3)=4^-3x^-3y^6#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(a^-m=1/a^m)color(white)(2/2)|)))#

#rArr4^-3x^-3y^6=1/4^3xx1/x^3xxy^6/1#

#=(1xx1xxy^6)/(4^3xxx^3xx1)=(y^6)/(64x^3)#

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