ShmoopTube

00:02

Put this in your calculator and shmoop it...

00:05

If x to the y power... to the y power... to the y power...

00:10

to the y power... equals x to the 81st power... then y can be which of the following?

00:17

And here are the potential answers...

00:23

There may be a lot of parentheses here, but don't panic.

00:25

All we need is a simple exponent rule. Remember this rule?

00:31

When we take an exponent to an exponent, all we have to do is multiply the two exponents together.

00:38

So x to the y to the y is the same thing as x to the y squared.

00:44

So x to the y squared to the y to the y is the same thing as x to the y to the fourth power.

00:53

The base of both sides are the same, so the exponents of both sides must be the same.

01:00

Yeah, probably.

01:01

So y to the fourth is equal to 81.

01:03

What number, to the fourth power, is 81?

01:06

Well, 3 times 3 is 9 times 3 is 27 times 3 is 81, but

01:10

3 isn't the only number that's equals 81 when raised

01:14

to the fourth power. What's another one that works?

01:18

Negative 3 to the fourth power is also 81.

01:21

The negative cancels out since the exponent is even.

01:25

So yep, E is our answer.

Full Transcript