Question

Please give an explanation with you answer, thank you :)

Answer 1

For this case we have the following expression:
24 ^ (1/3)
Rewriting we have:
3 ^ root (24)
3 ^ root (2 * 2 * 2 * 3)
3 ^ root (2 ^ 3 * (3))
Then, by properties of exponents we have:
2 * (3 ^ root (3))
Answer:
2 * (3 ^ root (3))
option 2

Answer 2

Answer:
2∛3 which is the second choice

Step-by-step explanation:
before we begin, remember the following:
√xy = √x * √y
(xy)ᵃ = xᵃ * yᵃ
∛x = x^(1/3)

Now, for the given, we have:

`24^ (1)/(3)`

24 can be rewritten as 8 * 3

Therefore, the given is now:

`(8*3)^ (1)/(3)`

Distributing the power:

`8^ (1)/(3) * 3^ (1)/(3)`

We know that:
∛8 = 2

Therefore, the simplest form of the given would be:

`8^ (1)/(3) * 3^ (1)/(3)`
2 *
`3^ (1)/(3)`
2∛3

Hope this helps :)