Question

Which expression is equivalent to 24∧ 1/3?

Answer 1

It should be the third root of 24 or 2 on the outside of the third root of 3

Answer 2

`2\sqrt[3]{3}`.

Explanation:

We have been given an expression
`24^{(1)/(3)}`. We are supposed to express our given expression in another form.

Using exponent property
`a^{(1)/(n)=\sqrt[n]{a}`, we can write our given expression as:

`24^{(1)/(3)}=\sqrt[3]{24}`

We can write 24 as product of 8 and 3.

`24^{(1)/(3)}=\sqrt[3]{8\cdot 3}`

`24^{(1)/(3)}=\sqrt[3]{2^2\cdot 3}`

Using exponent property
`\sqrt[n]{a^n}=a`, we will get:

`24^{(1)/(3)}=2\sqrt[3]{3}`

Therefore, the equivalent expression is
`2\sqrt[3]{3}`.