Question

How do you simplify \[{8^{\dfrac{4}{3}}}\] ?

Answer 1

Hint:
For solving this type of question we just need to rewrite the power in such a way that the fraction gets removed and in this question we will use the properties which will be ${\left( {{a^b}} \right)^c} = {a^{bc}}$, and we will rewrite the $8$ in its prime factorization.

Formula used:
Property of power,
${\left( {{a^b}} \right)^c} = {a^{bc}}$
Here, $a$ will be the base and $b\& c$ will be the power.

Complete step by step solution:
First of all we will calculate the factor of $8$ , it will be equal to
$ \Rightarrow 8 = 2 \cdot 2 \cdot 2$
And the above equation can be written in the form of power as
$ \Rightarrow 8 = {2^3}$
So by substituting this value in the question, the question will become
\[ \Rightarrow {\left( {{2^3}} \right)^{\dfrac{4}{3}}}\]
Now on removing the braces, we will get the equation as
\[ \Rightarrow {2^{3 \times \dfrac{4}{3}}}\]
Since, the like term will cancel each other, therefore the equation will be written as
\[ \Rightarrow {2^4}\]
And on solving the power, we will have the value equal to
$ \Rightarrow 16$

Hence, on simplifying \[{8^{\dfrac{4}{3}}}\] we get $16$ as a value.

Note:
For solving this type of question we don’t need to know the high level calculation, we just need to think about what we should change in it so that we can solve it easily. Like sometimes by changing the base we can solve questions. So with practice this will come.