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5 votes
Which expression is equivalent to 24 Superscript one-third?

2 Answers

4 votes

Answer:


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

User Christian Dechery
by
8.1k points
5 votes

Answer:

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}

User Ahamed Ishak
by
8.3k points

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