How do you simplify #(\frac { 3x } { y } ) ^ { 4} (\frac { x ^ { - 8} } {( x y ) ^ { 3} } ) ^ { 2}#?

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Answer 1 · 2016-10-20T04:17:48

The answer is #color(blue)(18/(x^(18)y^10))#.

Simplify: #((3x)/(y))^4 ((x^(-8))/((xy)^3))^2#.

Multiply the exponents outside the parentheses times the terms inside the parentheses.

#(((3x)^4)/(y^4)) (x^(-16)/(xy)^6)#

Simplify #(3x)^4# to #81x^4#.

#((18x^4)/(y^4)) (x^(-16)/(xy)^6)#

Simplify #(xy)^6# to #x^6y^6#.

#(18x^4)/(y^4)*(x^(-16))/(x^6y^6)#

Multiply the numerators and denominators, adding the exponents on like bases.

#(18x^(4+(-16)))/(x^(6)y^(4+6)#

Simplify.

#(18x^(-12))/(x^(6)y^10#

Subtract exponents in the denominator from exponents in the numerator with the same base.

#(18x^(-12-6))/y^10#

#(18x^(-18))/y^10#

Apply the negative exponent rule.

#18/(x^(18)y^10)#