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

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Answer 1 · 2017-05-20T17:25:35

#frac(7)(32 y^(15))#

We have: #(frac(3 x^(2) y^(- 2))(2 x y))^(3) (frac(2 x^(3) y^(3))(x^(- 2)))^(- 2)#

Using the laws of exponents:

#= (frac(7 x^(6) y^(- 6))(8 x^(3) y^(3))) (frac(frac(1)(4) cdot x^(- 6) cdot y^(- 6))(x^(- 4)))#

#= frac(7 cdot frac(1)(4))(8) cdot x^(6 + (- 6) - 3 - (- 4)) cdot y^(- 6 + (- 6) - 3)#

#= frac(frac(7)(4))(8) cdot x^(6 - 6 - 3 + 4) cdot y^(- 6 - 6 - 3)#

#= frac(7)(32) cdot x ^(1) cdot y^(- 15)#

#= frac(7)(32 y^(15))#