Question

how do you solve 16^(-3/4) without a calculator?

Answer 1

split the powers and then do individually

Answer 2

what do you mean by split the powers?

Answer 3

do u got it

Answer 4

no, im lost where -3 is multiplyed by 6 and then the ^1/4 part

Answer 5

ok i explain in steps

Answer 6

(-3) means \[\frac{1}{16^3}\] and (1/4) means \[\sqrt[4]{16}\] right?
So, since you're doing both to the 16...
it can be written as
\[\frac{1}{\sqrt[4]{16^3}}\]
or
\[\frac{1}{\sqrt[4]{16}^3}\]

Answer 7

that makes sense so far

Answer 8

Now, one looks much more easy to solve than the other, even though they are the same thing.

Answer 9

the power is -3/4
base is 16
now 16^-3 . 16^1/4=1/(16)^3.\[\sqrt[4]{16}\]

Answer 10

how does \[\sqrt[4]{16^3}\] turn into 8?

Answer 11

i know the answer is 1/8

Answer 12

\[\sqrt[4]{4096}\]

Answer 13

nvm

Answer 14

I would look at it the other way - just to avoid that huge number \[16^3\].

Answer 15

\[\frac{1}{\sqrt[4]{16}^3}\]

Answer 16

So it's like
\[\frac{1}{(\sqrt[4]{16})^3}\]

Answer 17

And what is \[\sqrt[4]{16}\]?

Answer 18

Guess :P

Answer 19

It's a nice number.

Answer 20

2

Answer 21

sorry, i was afk for a while

Answer 22

then 2^3 is 8

Answer 23

so 1/8

Answer 24

thanks!

Answer 25

Understood! Thank you! And you're welcome!