How do you simplify x^-4/(2xy^3*(2x^3y^2)^3)?

1 Answer
Jan 11, 2017

1/(16x^14y^9)

Explanation:

Before we start note that 2 is the same as 2^1

color(blue)("Consider "x^(-4))

x^(-4) is the same as 1/x^4

As an additional point: 1/x^(-4) is the same as x^4
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color(blue)("Consider "(2x^3y^2)^3

This is the same as (2x^3y^2)xx(2x^3y^2)xx(2x^3y^2)

Giving:" "8x^9y^6

So as a general case:" "(x^ay^b)^c = x^(axxc)y^(bxxc)
So for (2x^3y^2)^3 = 2^(1xx3)x^(3xx3)y^(2xx3)

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color(blue)("Putting it all together")
x^-4/(2xy^3(2x^3y^2)^3) = 1/x^4xx 1/(2xy^3(2x^3y^2)^3)=1/x^4xx1/(2xy^3xx8x^9y^6)

" "=1/(16x^14y^9)