Question

Which expression is equivalent to 24 Superscript one-third?

Answer 1

Answer:

$24^{1/3}$ = $\sqrt[3]{24}$ or $2\sqrt[3]{3}$

Step-by-step 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

Answer:

See explanation

Step-by-step explanation:

The given expression is: $(24)^{\frac{1}{3}}$

Recall that 24=3*8

$\implies(24)^{\frac{1}{3}}=(8*3)^{\frac{1}{3}}$

Recall again that:

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

$\implies (8*3)^{\frac{1}{3}}=(8)^{\frac{1}{3}}*(3)^{\frac{1}{3}}$

$\implies (8*3)^{\frac{1}{3}}=(2^3)^{\frac{1}{3}}*(3)^{\frac{1}{3}}$

$\implies (8*3)^{\frac{1}{3}}=2^{3*\frac{1}{3}}*(3)^{\frac{1}{3}}$

$\implies (8*3)^{\frac{1}{3}}=2*(3)^{\frac{1}{3}}$

We rewrite in radical form to obtain

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