Question

evaluate 64^-2/3 (Alg II. I award medals)

Answer 1

Hint: \[\huge x^{-n} = \frac{ 1 }{ x^n }\]

Answer 2

\[\frac{ 1 }{ 64^{2/3} } ???\]

Answer 3

Yeah, can you keep going?

Answer 4

First of all, remember to factor 64.

Answer 5

\[
64=2\times 32\\
32 = 2\times 16 \\
16 = 2\times 8\\ \ldots
\]

Answer 6

okay so 2 & 32... do I factor further?

Answer 7

You could also use the rule that for x^m/n is the same as the n (root of x)^m

So for 64^2/3, it would be (3(sqrt 64))^2

So you would find the cube root of 64, then square it

Answer 8

... but it's negative

Answer 9

Not when you use Astrophysic's formula

Answer 10

but the answer is 1/16 and that would be 1/27

Answer 11

\[\frac{ 1 }{ 64^{2/3} } =\frac{ 1 }{(\sqrt[3]{64})^2 } = \frac{ 1 }{ (4)^2 } =?\]

Answer 12

any doubts?

Answer 13

@study_buddy99 hope u understood.. so what will be the answer?

Answer 14

16

Answer 15

u mean" 1/ 16 "! thats correct!

Answer 16

yay! Thank you!