Question

Which expression is equivalent to 24 Superscript one-third?

Answer 1

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

Explanation:

We will apply one of the laws of indices which states

`a^(b/c)` =
`\sqrt[c]({a})^b`

So from the question given, 24 superscript one-third =
`24^(1/3)`

by comparison, a= 24, b = 1, and c = 3

Applying the law I stated above

`a^(b/c)` =
`\sqrt[c]({a})^b`

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

`a^(b/c)` =
`\sqrt[3]({8 X 3})^(1)`

`a^(b/c)` =
`\sqrt[3]({8})^(1)` ×
`\sqrt[3]({3})^(1)`

`a^(b/c)` = 2 ×
`\sqrt[3]({3})^(1)`

`2\sqrt[3]{3}` (superscript 1 is removed because any value raised to the power of one is equal to that value) or
`\sqrt[3]{24}`

Therefore the expression will be
`2\sqrt[3]{3}` or
`\sqrt[3]{24}` ---- Answer

Answer 2

See explanation

Explanation:

The given expression is:
`(24)^{(1)/(3)}`

Recall that 24=3*8

`\implies(24)^{(1)/(3)}=(8*3)^{(1)/(3)}`

Recall again that:

`(a*b)^n=a^n*b^n`

`\implies (8*3)^{(1)/(3)}=(8)^{(1)/(3)}*(3)^{(1)/(3)}`

`\implies (8*3)^{(1)/(3)}=(2^3)^{(1)/(3)}*(3)^{(1)/(3)}`

`\implies (8*3)^{(1)/(3)}=2^{3*(1)/(3)}*(3)^{(1)/(3)}`

`\implies (8*3)^{(1)/(3)}=2*(3)^{(1)/(3)}`

We rewrite in radical form to obtain

`\implies (8*3)^{(1)/(3)}=2\sqrt[3]{3}`