Question

How do you write $\sqrt[5]{8}$ in rational exponential notation?

Answer 1

Hint: In this question we have been asked to write the given mathematical expression $\sqrt[5]{8}$ in rational exponential notation. From the basic concepts of algebra we know that we can write the mathematical expression $\sqrt[n]{a}$ as ${{a}^{\dfrac{1}{n}}}$ in rational exponential notation.

Complete step by step answer:
Now considering from the question we have been asked to write the given mathematical expression $\sqrt[5]{8}$ in rational exponential notation.
From the basic concepts of algebra we know that we can write the mathematical expression $\sqrt[n]{a}$ as ${{a}^{\dfrac{1}{n}}}$ in rational exponential notation. Now we will use this in the process of our solution.
By using this concept we will have $\sqrt[5]{8}$ as $\Rightarrow \left( {{8}^{\dfrac{1}{5}}} \right)$ .
This can be further simplified and written as $\Rightarrow {{\left( {{2}^{3}} \right)}^{\dfrac{1}{5}}}$ because $8={{2}^{3}}$ .
Therefore we can conclude that the given mathematical expression $\sqrt[5]{8}$ can be written as ${{2}^{\dfrac{3}{5}}}$ in rational exponential form.

Note: While answering questions of this type we should be sure with the concepts that we are going to apply in the process. This is a very simple and easy question and can be answered accurately in a short span of time. Very few mistakes are possible in questions of this type. Similarly we can write $\sqrt[4]{16}$ as ${{16}^{\dfrac{1}{4}}}$ by using the concept stating that $\sqrt[n]{a}={{a}^{\dfrac{1}{n}}}$ . This can be further simplified and written as ${{\left( {{2}^{4}} \right)}^{\dfrac{1}{4}}}$ which can be simply stated as 2. Similarly we can express any kind of expression in the form of rational exponential notation.