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]
