Question

how do I calculate 8 to the power of 2/3? Please show calculations, thanks

Answer 1

First look at this thing:

\(\Rightarrow\large {8^{2 \over 3} = 8^{1\over 3} \times 8^{1 \over3} } \)

Do you agree with this statement?

Answer 2

ok, i follow

Answer 3

Okay. So, do you know what \(8^{1 \over 3}\) is?

Answer 4

4?

Answer 5

No. \(8^{1 \over 3} = \sqrt[3]{8}\). Do you know what the cube root of 8 is?

Answer 6

Sorry, that's the answer to 8 to the power of 2/3. I'm not sure how to calculate the cube root by hand. We not allowed to use calculators.

Answer 7

Cube root of 8 is the number you multiply to itself three times and get 8.

Answer 8

Cube root of 1000 is 10, because 10 x 10 x 10 = 1000.

Answer 9

ok, so 2^3 = 8

Answer 10

Yes, so cube root of 8 is 3.
Return back to what I said.

\(\Large 8^{2 \over 3} = 8^{1 \over 3} \times {8^{1 \over 3} = 2 \times 2}\)

Answer 11

mmm, cube root of 8 is 2? Check your answer. Excellent explanation, thanks

Answer 12

Thanks, and no problem.

Answer 13

What's 2 x 2? That'd be the final answer.

Answer 14

:-) Thanks I get it.

Answer 15

You're welcome!

Answer 16

Does it work the same for negative numbers? Say (-8) to the power of 1/3? Just for interest sake...

Answer 17

Yeah, cube root of -8 is -2.

Answer 18

Ok, cool. Thanks again, cheers

Answer 19

Cheers! Bring in the wine, eh?

Answer 20

lol... ok, ciao