Question

What is the simplified value of the exponential expression 24 1/3

Answer 1

Hi!

I think you mean $24^{\frac{1}{3} }$

Which can be simplified to

∛24

Because the 3rd root of 24 is equal to $24^{\frac{1}{3} }$.

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Now remove all the cube roots from the expression by factorizing 24.

24/2 = 12

12/2 = 6

6/2 = 3

3/3 = 1

24 = 2 * 2 * 2 * 3

24 = 2³ * 3

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Now we have ∛2³ * ∛3

Simplify

2 * ∛3

2∛3

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The answer is 2∛3

Hope this helps! :)

-Peredhel

Answer 2

Remark

Does this mean  y = (24)^(1/3) ?

If it does then factor 24 into it's prime factors.

Solve

24 = 2*2*2 * 3

Put the results under the cube root sign.

∛(2 * 2 * 2 * 3)

For every 3 equal factors you get to take 1 outside the root sign. You discard the other 2. You then leave the 3 alone.

2∛3 is your answer.

Another way to do this is to realize that the cube root of 8 = 2

∛(8 * 3) = ∛8 * ∛3 = 2*∛3