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

1 Answer
Jim G.
Nov 18, 2016

#(4x^7)/(9y^(10))#

Explanation:

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

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

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

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(a^mxxa^n=a^(m+n)" and " a^-mhArr1/a^m)color(white)(2/2)|)))#

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

#=1/3^2xxx^4xx1/y^6xx4xxx^3xx1/y^4#

#=1/9xx4xxx^4xxx^3xx1/y^6xx1/y^4#

#=(1xx4xxx^7)/(9xxy^6xxy^4)=(4x^7)/(9y^(10)#

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