Question

Simplify \[{{9}^{\dfrac{3}{2}}}\].

Answer 1

Hint: In the above type of question when the power is in fraction try to use the denominator first with base i.e. if the value of denominator can give a numerical value then use the power in numerator so as to give out the final value.

Complete step by step answer:
In the above question we will first check whether the base that is x in this \[{{x}^{a}}\] can give out numerical value when solved with the denominator value of the a. So in this question we can see that the base value which is 9 when applied the denominator value which is 2 give us a numerical value 3 as when power \[\dfrac{1}{2}\] is none other than square root of the number and as we know that the square root of 9 is 3 so we got the final value of the base as 3 and we also have gotten rid of the denominator value of the power that was there with the base. Now as the value of base has been changed and the new value came as \[{{3}^{3}}\], we can clearly see that we need to find the cubic value of 3 which is none other than 3x3x3 and when we solve this 3x3x3 we will get the final value of the question asked above so we get the final value of the question asked above is equal to \[{{3}^{3}}=27\]

So after simplification of the above question which was \[{{9}^{\dfrac{3}{2}}}\] we got the value as 27.

Note: In the above question we generally apply the denominator value after we have applied the numerator value, now to simplify this always prefer to use the denominator value first then go for the numerator as it will help you get to the answer in a faster and easier way.