ShmoopTube

00:03

Here's a shmoop du jour for you and your... brain.

00:07

Which of the following is equivalent to 27 cubed times 3 over 243 squared?

00:15

And here are the potential answers...

00:21

OK, so what is this question testing?

00:23

Well, really it's testing how good we are at our multiplication tables, especially the

00:27

column that deals with the number 3.

00:30

We could certainly brute force this question

00:31

and multiply 27 times 27 times 27.

00:35

We could also square 243.

00:37

But that won't scale for harder, bigger problems...

00:40

So let's try to do this the fancy, dancy... correct way...

00:44

and rewrite it as 3 cubed, which is 27.

00:47

Yep, 3 times 3 is 9... times 3 is 27 -- then cube the whole thing.

00:52

Then there's that 243 fella -- such a strange, random-looking number.

00:57

It should feel 'fishy' -- and if you were in the super advanced multiplication

01:01

tables group and played out that 3 times thing...

01:04

...you'd remember that 3 times 27 is 81... and 81 times 3 is -- yes -- ding ding ding.

01:10

So rewrite 243 as 3 to the 5th power.

01:14

Or rather, rewrite the whole problem now to look like this:

01:19

Now it's just about multiplying the exponents.

01:21

We get 3 to the 9th times the quantity 3 over 3 to the 10th.

01:26

Yet another curveball on this very gnarly problem -- remember that when multiplying

01:31

exponents, we can ADD the powers... AND remember that 3 is 3 to the FIRST power.

01:37

So we can rewrite the problem again as 3 to the 9th times 3 to the first... to get 3 to the 10th.

01:43

So what gives? We have 3 to the 10th over 3 to the 10th --

01:47

yeah -- a whole lotta work just to get... 1.

01:50

But at least we can get there by counting our fingers.

01:53

And... we're done. The answer is C.

Full Transcript