Question

How do you simplify \[{8^{\dfrac{1}{3}}}\].

Answer 1

Hint:In this question, we will use the concept of the base power to simplify the given operation. In this question, first, factorize the given base number and write it in the form of the power and simplify the number by using the standard identities.

Complete step by step answer:
In this question, we have given an operation that needs to be simplified: the given operation is ${8^{\dfrac{1}{3}}}$.
Then, simply we will use a formula and the formula is given below.
$A$ is the base and $c$ is its power. Then it can be written as \[{\left( A \right)^c}\].
First, we find the factor of the base. If the Base has the same number of factors. Then count the same number factor and take them one and write the power.
If A has repeated factor a and reached up b time.
Then, \[{\left( A \right)^c}\]is written as below.
\[ \Rightarrow {\left( A \right)^c} = {\left( {{a^b}} \right)^c}\]
Then, after simplifying this \[{\left( {{a^b}} \right)^c}\] we can write it as given below.
\[ \Rightarrow {\left( {{a^b}} \right)^c} = {\left( a \right)^{b \times c}}\]
As per the given question we have,
Where,
\[
  A = 8 \\
  c = \dfrac{1}{3} \\
 \]
First, we find the factor of \[8\]
Then,
The factor of \[8\] is \[ = 2 \times 2 \times 2\].
Where,
\[
  a = 2 \\
  b = 3 \\
 \]
Now we will put these values in the above formula,
Hence,
\[ \Rightarrow {\left( {{2^3}} \right)^{\dfrac{1}{3}}} = {\left( 2 \right)^{3 \times \dfrac{1}{3}}}\]
After calculating the above expression, the result is \[2\].

Therefore, after simplifying the result of \[{8^{\dfrac{1}{3}}}\] is \[2\].

Note: As we know that if we want to simplify the power of the base problem, then first we check the factor of the base if the base is written in repeating factor. Then you can simply use that formula for calculating that type of problem. And the formula is given below.
\[ \Rightarrow {\left( {{a^b}} \right)^c} = {\left( a \right)^{b \times c}}\].