Question

Find the value of \[{4^{\dfrac{3}{2}}}\]?

Answer 1

Hint: Here we need to solve the given term of expression by simplifying the power to the number, here we can see that the number given is four which can be written as two to the power two and then solve further by using some properties of exponent.
Formulae Used: \[ \Rightarrow {({a^m})^{\dfrac{x}{y}}} = {a^{m \times \dfrac{x}{y}}}\]

Complete step-by-step solution:
Here the given question is to simplify the expression which is given for the number four, and a fraction power is given to the number, in order to solve the power we need to use the property of exponent and we have to break the given number four also to simplify the given expression, on solving we get:
$\Rightarrow {4^{\dfrac{3}{2}}} $
Here we write the 4 in form of 2 to the power 2 to simplify the expression.
\[= {({2^2})^{\dfrac{3}{2}}} \]
\[= {2^{2 \times \dfrac{3}{2}}} \]
\[= {2^{\dfrac{3}{1}}} \]
\[= {2^3} = 8\]
Here we get the simplified expression value as eight.

Note: In order to deal with the expression which contains powers and fraction terms, we need to simplify the given term into the simplest form to get the value and to do such simplification we need to sometimes use certain properties too in order to simplify and get the result.