How do you simplify #\frac { ( 2x ^ { - 3} y ^ { - 2} ) ^ { 5} } { ( 6x ^ { - 1} y ^ { - 8} ) ^ { 2} }#?

1 Answer
Jim G.
Nov 8, 2016

#(8y^6)/(9x^(13)#

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((2x^-3y^-2)^5)/((6x^-1y^-8)^2)#

#=(2^((1xx5))x^((-3xx5))y^((-2xx5)))/(6^((1xx2))x^((-1xx2))y^((-8xx2))#

#=(2^5x^(-15)y^(-10))/(6^2x^-2y^(-16)#

#=32/36xxx^(-15)/x^-2xxy^(-10)/y^(-16)#

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

#rArr=8/9xxx^((-15-(-2)))xxy^((-10-(-16))#

#=8/9xxx^(-13)xxy^6=8/9xx1/x^(13)xxy^6/1=(8xx1xxy^6)/(9xxx^(13))#

#=(8y^6)/(9x^(13))#

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