Question

How do you write the expression $\sqrt[4]{v}$ in exponential form?

Answer 1

Hint: Here, in this question we are supposed to convert the given radical expression into its equivalent exponential form. In order to do that, we are required to identify the base in the expression and then, we have to identify the power and raise the base to that power.

Complete step-by-step solution:
For solving this question, the concept of radical expressions and exponential expressions must be clear to the students. Those expressions which contain the radical symbol $\sqrt[n]{{}}$are known as radical expressions. The power is written just outside the radical symbol, taking the place of $n$ whereas the base is written inside the symbol. The power is represented in the form of $\dfrac{1}{n}$.
Those expressions which can be expressed in the form of ${A^b}$, where $A$ is base and $b$is power are called exponential expressions. Here, in this question, the number/term which is inside the radical symbol is the base. Since the number/term given inside radical is $v$, so $v$ is our base.
We know that the number just outside the radical symbol will be our power. As we can clearly see that the number $4$is given outside radical symbol, so, our power will be $4$. We can conclude it to be a fourth root.
Now, we know that the way of representing exponentials is by ${A^b}$.
First, we have to substitute $v$ for $A$ and $\dfrac{1}{4}$ for $b$ in expression ${A^b}$.
By doing so, we get ${v^{\dfrac{1}{4}}}$.

Hence, exponential form which is equivalent to radical expression $\sqrt[4]{v}$ is ${v^{\dfrac{1}{4}}}$.

Note: A radical symbol $\sqrt {} $is only used when we have to represent a radical expression but most of the time students misread it as a square root symbol. Apart from square roots, this radical symbol can also be used to denote cube root, fourth root or higher roots whose numbers are written in their place accordingly.