# How do you simplify 6/w^3div6/w^4?

Nov 2, 2017

By arranging. Your result is w.

#### Explanation:

$\frac{\frac{6}{w} ^ 3}{\frac{6}{w} ^ 4}$

$= \frac{6 \times {w}^{4}}{6 \times {w}^{3}} = w$

Since $\frac{6}{6} = 1$

and $\frac{{w}^{4}}{{w}^{3}} = \frac{w \times {w}^{3}}{{w}^{3}} = w$

Nov 2, 2017

$w$

#### Explanation:

$\text{note that for division of fractions}$

$\text{we can convert to multiplication as follows}$

•color(white)(x)a/b-:c/d=a/bxxd/c

$\Rightarrow \frac{6}{w} ^ 3 \div \frac{6}{w} ^ 4$

$= \frac{6}{w} ^ 3 \times {w}^{4} / 6$

$\textcolor{b l u e}{\text{cancelling common factors}}$

$= {\cancel{6}}^{1} / {w}^{3} \times {w}^{4} / {\cancel{6}}^{1} = {w}^{4} / {w}^{3} = {w}^{\left(4 - 3\right)} = w$

Nov 2, 2017

$w$

#### Explanation:

If you wish to understand why the shortcut method works have a look at: https://socratic.org/s/aKvaM7cE

The shortcut is: turn $\frac{6}{w} ^ 4$ upside down and multiply giving:

$\frac{6}{w} ^ 3 \times {w}^{4} / 6$

cancelling out

$\frac{\cancel{6}}{\cancel{{w}^{3}}} \times {w}^{\cancel{4}} / \cancel{6} = w$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b r o w n}{\text{This is why "cancel(6)/cancel(w^3)xx w^(cancel(4))/cancel(6) = w color(white)("d")" works}}$

$\frac{6}{w} ^ 3 \times {w}^{4} / 6 \textcolor{w h i t e}{\text{ddd") -> color(white)("ddd}} \frac{6}{6} \times {w}^{4} / {w}^{3}$

$\textcolor{w h i t e}{\text{ddddddddddd")->color(white)("d}} 1 \times \frac{w \times {w}^{3}}{w} ^ 3$

$\textcolor{w h i t e}{\text{ddddddddddd")->color(white)("d}} 1 \times w \times {w}^{3} / {w}^{3}$

$\textcolor{w h i t e}{\text{ddddddddddd")->color(white)("d}} 1 \times w \times 1 = w$