Question

How do you simplify ${{32}^{\dfrac{1}{5}}}$ ?

Answer 1

Hint: In the above question, you were asked to simplify ${{32}^{\dfrac{1}{5}}}$ . You have to use exponent law for solving this problem. The exponent says how many times to use the number in a multiplication. So, let us see how we can solve this problem.

Complete step-by-step answer:
The given problem statement is to simplify${{32}^{\dfrac{1}{5}}}$.
Let a be any variable and a = ${{32}^{\dfrac{1}{5}}}$ , hence $a{}^{5}=32$
Also, 2 . 2 . 2 . 2 . 2 = ${{2}^{5}}$ = 32
 $\therefore {{a}^{5}}={{2}^{5}}$
As, both the bases of power is same, hence, a = 2
Therefore, the fifth root of 32 is 2.

Additional Information:
In the above question, we used exponent law. There are several other exponent laws such as Multiplication rule, Division rule, Zero exponents, Negative exponent, Fractional exponent, power of a power rule, Power of a product rule, and power of a fraction rule. These small laws are quite helpful in solving the problem.

Note: In the above problem, we were asked to simplify the fifth root of 32. Also, 5 times of 2 is equal to 32, therefore from the exponent law, we concluded that a is 2. This problem could not be solved without the help of a variable that’s why we took a variable a.