Question

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

Answer 1

By arranging. Your result is w.

Explanation:

`(6/w^3)/(6/w^4)`

`=(6timesw^4)/(6timesw^3) = w`

Since `6/6 = 1`

and `(w^4)/(w^3) = (wtimesw^3)/(w^3) = w`

Answer 2

`w`

Explanation:

`"note that for division of fractions"`

`"we can convert to multiplication as follows"`

`•color(white)(x)a/b-:c/d=a/bxxd/c`

`rArr6/w^3-:6/w^4`

`=6/w^3xxw^4/6`

`color(blue)"cancelling common factors"`

`=cancel(6)^1/w^3xxw^4/cancel(6)^1=w^4/w^3=w^((4-3))=w`

Answer 3

`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 `6/w^4` upside down and multiply giving:

`6/w^3xx w^4/6`

cancelling out

`cancel(6)/cancel(w^3)xx w^(cancel(4))/cancel(6) = w`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("This is why "cancel(6)/cancel(w^3)xx w^(cancel(4))/cancel(6) = w color(white)("d")" works")`

`6/w^3xx w^4/6 color(white)("ddd") -> color(white)("ddd") 6/6xxw^4/w^3`

`color(white)("ddddddddddd")->color(white)("d")1xx(wxxw^3)/w^3`

`color(white)("ddddddddddd")->color(white)("d")1xxwxxw^3/w^3`

`color(white)("ddddddddddd")->color(white)("d")1xxwxx1 = w`