Question

Simplify ${{8}^{\dfrac{2}{3}}}$ ?

Answer 1

Hint: Here in this question we have been asked to simplify the given expression ${{8}^{\dfrac{2}{3}}}$ . For doing that we will express $8$ as ${{2}^{3}}$ . By doing this we will have ${{\left( {{2}^{3}} \right)}^{\dfrac{2}{3}}}$ then we can simplify this expression further then we will have ${{2}^{2}}$ . For getting the final conclusion we will multiply two with itself two times that is we will perform squaring of two.

Complete step by step answer:
Now considering from the question we have been asked to simplify the given expression ${{8}^{\dfrac{2}{3}}}$ .
For doing that we will express $8$ as ${{2}^{3}}$ .
By doing this substitution we will have ${{\left( {{8}^{3}} \right)}^{\dfrac{2}{3}}}$ then we can simplify this expression further then we will have ${{8}^{2}}$ .
For getting the final conclusion we will multiply two with itself two times that is we will perform squaring of two.
Now by performing squaring we will have $2\times 2$ .
After performing basic arithmetic multiplication operation for further simplifying we will have $4$ as the answer.

Therefore we can conclude that the simplified and reduced form of ${{8}^{\dfrac{2}{3}}}$ will be given as $4$.

Note: During the process of answering questions of this type we should be very careful with the simplifications we perform in between. 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. Someone can consider $8={{2}^{2}}$ by mistake and end up having a mess.