Question

How do you simplify $ {{3}^{\dfrac{7}{6}}} $ ?

Answer 1

Hint: For answering this question we need to simplify $ {{3}^{\dfrac{7}{6}}} $ by using simple mathematics by applying simple algebraic calculations like reducing the given expression in terms of simple number rather than exponents which will help us while performing further calculations on expressions of this type. For squaring this expression we will multiply this expression as per the value of its power and obtain the result which is known as the square of the expression.

Complete step by step answer:
Now considering from the question we have been asked to simplify $ {{3}^{\dfrac{7}{6}}} $ .
For simplifying this we will use simple algebraic calculations and simplify the given expression.
The simplifications are made just to reduce the given expression into some simplified form which will be useful while performing further calculations on this type of number.
Firstly we will perform the reduction of the given expression in terms of simple number rather than exponents of the given expression $ {{\left( 4{{a}^{3}} \right)}^{2}}=\left( 4{{a}^{3}} \right)\left( 4{{a}^{3}} \right) $ .
We will further simplify this by performing multiplication algebraic expressions using basic mathematics.
After further simplifying this expression we will have $ {{3}^{1+\dfrac{1}{6}}}=3\times {{3}^{\dfrac{1}{6}}} $ .
Now after the above calculation we can come to a further conclusion.
Therefore after all the above calculations and simplifications we can conclude that the simplified expression of $ {{3}^{\dfrac{7}{6}}} $ we will have $ 3\sqrt[6]{3} $ .

Note:
 We should be sure with our calculations and be aware while applying the simple algebraic concepts for answering questions of this type. Similarly, we can simplify other expressions too like $ {{2}^{\dfrac{5}{4}}} $ after simplifying this reference example we will have $ 2\sqrt[4]{2} $ . This type of calculations and simplifications are useful while performing further calculations on expressions of this type.