Simplify the following index question?

Question

#(-3x^2y^3)^2/(2xy)^3 times (4x^4y^3)/ (xy)^3#

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Answer 1 · 2017-07-19T12:03:35

#frac(9 x^(2) y^(3))(2)#

We have: #frac((- 3 x^(2) y^(3))^(2))((2 x y)^(3)) times frac(4 x^(4) y^(3))((x y)^(3))#

Using the laws of exponents:

#= frac(9 x^(4) y^(6))(8 x^(3) y^(3)) times frac(4 x^(4) y^(3))(x^(3) y^(3))#

#= frac(9 times 4)(8) (x^(4 + 4 - 3 - 3) cdot y^(6 + 3 - 3 - 3))#

#= frac(36)(8) (x^(8 - 6) cdot y^(9 - 6))#

#= frac(9 x^(2) y^(3))(2)#