Question

evaluate 81^3/4

Can someone explain how to do that?

Answer 1

is that
\[81^{3/4}\]?

Answer 2

Yes

Answer 3

can you express 81 as a power of some number?

Answer 4

81 = ? ^ ??

Answer 5

This is essentially the same as \[\sqrt[4]{81^{3}}\]

Answer 6

9^2

Answer 7

good

81 = 9^2

can you also express

9 as a power of some number?

Answer 8

@Sepeario I know but idk how to solve that part.

Answer 9

3^2

Answer 10

@UnkleRhaukus is teaching you right now how to find the 4th root of 81. Then you will have to put this to the power of 3. It doesn't really matter what order you do it.

Answer 11

so you have

81 = 9^2 = (3^2)^2

can you simplify this?

Answer 12

remember that \[(a^n)^m=a^{n\times m}\]

Answer 13

3^2x2 = 3^4 = 81

Answer 14

very good

now you have show that

\[81^{3/4} = (3^4)^{3/4}\]

what happens next?

Answer 15

Idk :L

Answer 16

\[(3^4)^{3/4}=3^{4\times3/4}=3^{\dots} \]

Answer 17

3^3?

Answer 18

YES!

Answer 19

so the final answer is 3^3 = 27?

Answer 20

\[\color{red}\checkmark\]

Answer 21

Okay perfect not bad.

Answer 22

Can I try another one on my own?

Answer 23

and if you can tell me if it's right or not?

Answer 24

sure

Answer 25

16^5/4 = 2^4^5/4 so far right?

Answer 26

parentheses make it clearer

16^(5/4) = (2^4)^(5/4)

i'm pretty sure you mean this (which is right)

Answer 27

yes

Answer 28

so it's going to be 2^5 = 32

Answer 29

you got it!

Answer 30

Okay thanks so much bud!

Answer 31

\[\ddot\smile \]

Answer 32

Nice one rhaukus. That's how you do it