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

3 Answers
Nov 2, 2017

Answer:

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#

Nov 2, 2017

Answer:

#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#

Nov 2, 2017

Answer:

#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#