How do you simplify $\frac{4 x^{- 1}}{12 x^{2}}$ $(4x^-1)/(12x^2)$ ?

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Answer 1 · 2018-05-21T21:22:54

$\frac{1}{3} x^{- 3}$ $1/3x^-3$

We have the following:

$\frac{4 x^{- 1}}{12 x^{2}}$ $(color(purple)(4)color(blue)(x^-1))/(color(purple)(12)color(blue)(x^2))$

We can handle these expressions separately. The purple terms just simplify to

$\frac{1}{3}$ $color(purple)(1/3)$

And we can rewrite the blue expressions as follows:

$x^{- 1 - 2}$ $color(blue)(x^(-1-2))$

We have the same base on the top and bottom, so we can subtract the exponents. Thus, we have

$x^{- 3}$ $color(blue)(x^-3)$

Putting it all together, we get

$\frac{1}{3} x^{- 3}$ $1/3x^-3$

as our final answer.

Hope this helps!

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