Question

Simplify 27^-(2/3)

9

1/9

-1/9

−9

Answer 1

\[\LARGE (\frac{a}{b})^{-x}=(\frac{b}{a})^{x}\]

Answer 2

so i make the 9 into a frction like \[\frac{ 9 }{ 1 }\] then flip it?

Answer 3

Yup!

Answer 4

ok then what would i do with the -2/1 exponent?

Answer 5

i meant 2/3

Answer 6

When you flip the fraction, it just becomes positive.

Answer 7

would i multiply it with 9/1?

Answer 8

It goes like this:
First you flip the number to make the exponent positive
\[\LARGE 27^{-2/3}=(\frac{1}{27})^{2/3}\]
Now just distribute the exponent out to everything:
\[\LARGE a^{2/3}=\sqrt[3]{x^2}\]

Answer 9

but how would i get it to one of my answer choices

Answer 10

So what's 1^(2/3) and 27^(2/3)?

Answer 11

1^(2/3) is \[^{3}\sqrt{1^{2}}\] and the other is \[^{3}\sqrt{27^{2}}\]

Answer 12

Correct, now simplify them

Answer 13

how would i do that

Answer 14

Well 1 to any power 1. So that one is simple. For the 27, first take the cubic root of it.

Answer 15

so i square it then divide it by 3?im not sure how to do tht

Answer 16

Hmm, do you have a calculator?

Answer 17

yea it is on my computer.i have it up right now

Answer 18

Okay, type this in: 27^(1/3)

Answer 19

i got it.it is 3

Answer 20

Since \[\LARGE 27^{2/3}=27^{1/3*(2)}\]
Right, now sqaure that and you get..

Answer 21

*square

Answer 22

i get 9

Answer 23

Correct!
So our final answer is:
\[\LARGE \frac{1}{9}\]

Answer 24

thank you so much i really apreciate it

Answer 25

ANytime bud.

Answer 26

thanks man