Select the correct answer.

Which expression is equivalent to [tex]\sqrt[3]{5}[/tex]?
A. [tex]5^{\frac{1}{3}}[/tex]
B. [tex]5^3[/tex]
C. [tex]\frac{3}{5}[/tex]
D. [tex]\frac{5}{3}[/tex]



Answer :

To determine which expression is equivalent to [tex]\(\sqrt[3]{5}\)[/tex], let's break down the problem.

The notation [tex]\(\sqrt[3]{5}\)[/tex] represents the cube root of 5. In mathematical terms, finding the cube root of a number is the same as raising that number to the power of [tex]\(\frac{1}{3}\)[/tex].

Therefore:

[tex]\[ \sqrt[3]{5} = 5^{\frac{1}{3}} \][/tex]

Now, let's look at each option:

A. [tex]\(5^{\frac{1}{3}}\)[/tex] — This is exactly how we represent the cube root of 5 in exponential form.
B. [tex]\(5^3\)[/tex] — This means 5 raised to the power of 3, which is 5 multiplied by itself three times (i.e., [tex]\(5 \times 5 \times 5 = 125\)[/tex]). This is not equivalent to the cube root of 5.
C. [tex]\(\frac{3}{5}\)[/tex] — This is a fraction where 3 is divided by 5. This is not related to finding the cube root of 5.
D. [tex]\(\frac{5}{3}\)[/tex] — This is a fraction where 5 is divided by 3. This also does not relate to finding the cube root of 5.

Thus, the only expression that correctly represents [tex]\(\sqrt[3]{5}\)[/tex] is:

A. [tex]\(5^{\frac{1}{3}}\)[/tex]

So, the correct answer is:

A. [tex]\(5^{\frac{1}{3}}\)[/tex]