Question

How do you simplify ${16^{\dfrac{2}{4}}}$

Answer 1

Hint: In order to solve this question we will first solve the power which is in denominator and then we will calculate the answer coming then we will be applying the numerator’s power to that answer which was coming after the implementation of the denominator’s power will results to the final answer.

Complete step-by-step solution:
For solving this question we will first breakdown the powers into two parts that is we will separate the powers of numerator and denominator:
${\left( {{{\left( {16} \right)}^{\dfrac{1}{4}}}} \right)^2}$
It is not necessary to take the numerator’s power inside and the denominator’s power outside and can solve this question
As we were finding the root by prime factorization method so will apply here the same but as it was for square root we were taking two same terms to take one out from root here we will be taking four such same terms to take one out of that power:
${\left( {{{\left( {2 \times 2 \times 2 \times 2} \right)}^{\dfrac{1}{4}}}} \right)^2}$
Now we have converted it to factors so from here we will be taking only one 2 to outer bracket:
And hence the new term will be as follows:
${\left( 2 \right)^2}$
Now from here we will be simply squaring the term and will get the final answer as $4$

Hence the correct answer is $4$.

Note: While solving these types of questions we should be careful of the denominator’s power because there is a possibility of just taking the 1 out of root from two terms as we have done many times in roots. And we can also do it by first simplifying the power first and then solving it.