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

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

Now, for the given, we have:
$24^ \frac{1}{3}$

24 can be rewritten as 8 * 3

Therefore, the given is now:
$(8*3)^ \frac{1}{3}$

Distributing the power:
$8^ \frac{1}{3} * 3^ \frac{1}{3}$

We know that:
∛8 = 2

Therefore, the simplest form of the given would be:
$8^ \frac{1}{3} * 3^ \frac{1}{3}$ 
2 * $3^ \frac{1}{3}$ 
2∛3

Hope this helps :)