Question

What is \[\dfrac{1}{2}\] to the negative fourth power?

Answer 1

Hint: These types of questions are very easy to solve once we understand clearly the underlying and important concepts behind the problem. To solve this problem effectively we need to have some basic knowledge of fractions and power of fractions. In such problems what we need to do firstly is to convert the theoretical statement of the question into the mathematical form and then evaluate the result accordingly. The nth power of any number ‘a’ is generally represented in the form \[{{a}^{n}}\] . The negative power is represented as, \[{{a}^{-n}}\] , this can be further written as \[\dfrac{1}{{{a}^{n}}}\] . So here in this problem, what we need to find is the value of \[{{\left( \dfrac{1}{2} \right)}^{-4}}=\dfrac{1}{{{\left( \dfrac{1}{2} \right)}^{4}}}\] .

Complete step-by-step solution:
Now we start off with the solution to the given problem by writing that, we just need to evaluate the value of \[\dfrac{1}{{{\left( \dfrac{1}{2} \right)}^{4}}}\] . We can rewrite the given form of the problem as, \[{{2}^{4}}\] . To evaluate this value, we need to multiply \[2\] , \[4\] times and get the desired result. We evaluate it to get it as,
\[2\times 2\times 2\times 2=16\] . Thus our answer to the problem is \[16\] .

Note: This type of problem requires a bit of understanding of fractions and power of fractions. We need to be very careful while we invert the fraction when we are given any negative power. For given positive power the problem becomes very straight forward and can be solved very quickly. We must also keep in mind that when we are given any decimal value, the multiplication needs to be done with immense care or will result in a wrong solution.