Question

(1/512)^1/3

I know the answer is 1/8 but how do I get to that?

Answer 1

See explanation below

Answer is 1/8

Explanation:

The expression is:

`\left((1)/(512)\right)^{(1)/(3)}`

A number x raised to the power
`(1)/(3)` means it is the cube root of that number or
`\mbox{\large \sqrt[3]{x} }`

Also
`\left((1)/(x)\right)^a = ((1)^a)/(x^a)`

Combining these two facts we get

`\left((1)/(512)\right)^{(1)/(3)} = \frac{1^{(1)/(3)}}{512^(1)/(3)}= \frac{\sqrt[3]{1} }{\sqrt[3]{512} } = \frac{1}{\sqrt[3]{512} }`

`\sqrt[3]{512} = 8`

So

`\left((1)/(512)\right)^{(1)/(3)} = (1)/(8)`