Question

Find the value of ${125^{\dfrac{1}{3}}}.$

Answer 1

Hint: In order to find the value of give term, first we will try to make 125 in the form of some power so it will cancel out by outer power by using the formula as \[{({x^a})^b} = {x^{ab}}.\]

Complete step-by-step answer:
Given term is ${125^{\dfrac{1}{3}}}.$
Now, to evaluate this term we will write 125 as ${5^3}$
We know that if ${x^a}$ has power as b, then it can be written as \[{({x^a})^b} = {x^{ab}}.\]
By using this multiplying property we will proceed further
$
  \therefore {\left( {{5^3}} \right)^{\dfrac{1}{3}}} \\
   \Rightarrow {\left( 5 \right)^{3 \times \dfrac{1}{3}}} \\
    \\
$
Now, $3$ and $\dfrac{1}{3}$ will be cancel out with each other and we have
\[ \Rightarrow {\left( 5 \right)^1} = 5\]
Hence, the value of ${125^{\dfrac{1}{3}}}$ is 5.

Note: In order to solve these types of questions remember the basic properties of exponents. Some of these properties are when we raise a product to a power we raise each factor with a power. This is called the power of a product property. When we raise a quotient to a power we raise both the numerator and the denominator to the power. This is called the power of a quotient power. When we raise a number to a zero power we'll always get 1. Negative exponents are the reciprocals of the positive exponents.