Question: Bit of Everything

The rule, 1/(a/b) = b/a, is correct, but we don't have a 1/(a/b) situation here.

I'm using the fact that (a/b)/(c/d) = (a/b) x (d/c)

When dividing by a fraction, we multiply by the reciprocal.

That is: a/b ÷ c/d = a/b x d/c

So, for example: 2/3 ÷ 8/11 = 2/3 x 11/8

Likewise, (3/4)/(2/5) = (3/4)(5/2)

So, in the video solution, we have (16^something)/(1/27^something)

Applying the rule for dividing by fractions, we get:
(16^something)/(1/27^something) = (16^something)(27^something/1)
= (16^something)(27^something)

More here: https://www.greenlighttestprep.com/module/gre-arithmetic/video/1069

Does that help?

Cheers,
Brent

Nice work! Keep at it!!

Cheers,
Brent