Question

Simplify ${{25}^{\dfrac{3}{2}}}$ ?

Answer 1

Hint: Here in this question we have been asked to simplify the given expression ${{25}^{\dfrac{3}{2}}}$ . For doing that we will express $25$ as ${{5}^{2}}$ . By doing this we will have ${{\left( {{5}^{2}} \right)}^{\dfrac{3}{2}}}$ then we can simplify this expression further then we will have ${{5}^{3}}$ . For getting the final conclusion we will multiply five with itself three times that is we will perform cubing of five.

Complete step by step answer:
Now considering from the question we have been asked to simplify the given expression ${{25}^{\dfrac{3}{2}}}$ .
For doing that we will express $25$ as ${{5}^{2}}$ .
By doing this substitution we will have ${{\left( {{5}^{2}} \right)}^{\dfrac{3}{2}}}$ then we can simplify this expression further then we will have ${{5}^{3}}$ .
For getting the final conclusion we will multiply five with itself three times that is we will perform cubing of five.
Now by performing cubing we will have $5\times 5\times 5$ .
After performing basic arithmetic multiplication operation for further simplifying we will have $125$ as the answer.

Therefore we can conclude that the simplified and reduced form of ${{25}^{\dfrac{3}{2}}}$ will be given as $125$

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 $25={{5}^{3}}$ by mistake and end up having a mess.