How do you simplify 6/w^3div6/w^46w3÷6w4?

3 Answers
Nov 2, 2017

By arranging. Your result is w.

Explanation:

(6/w^3)/(6/w^4)6w36w4

=(6timesw^4)/(6timesw^3) = w=6×w46×w3=w

Since 6/6 = 166=1

and (w^4)/(w^3) = (wtimesw^3)/(w^3) = ww4w3=w×w3w3=w

Nov 2, 2017

ww

Explanation:

"note that for division of fractions"note that for division of fractions

"we can convert to multiplication as follows"we can convert to multiplication as follows

•color(white)(x)a/b-:c/d=a/bxxd/cxab÷cd=ab×dc

rArr6/w^3-:6/w^46w3÷6w4

=6/w^3xxw^4/6=6w3×w46

color(blue)"cancelling common factors"cancelling common factors

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