Question

How do you simplify $\sqrt[4]{{16}}?$

Answer 1

Hint: We know that the above given question is in exponential form. An exponent refers to the number of times a number is multiplied by itself. There is base and exponent or power in this type of equation. Here, in the given question $(\sqrt {16} )$ is the base. We can solve the given expression by the product rule. As we know that as per the property of exponent rule if there is $\sqrt[n]{{{a^m}}} = {a^{\dfrac{m}{n}}}$ . When we express a number in exponential form then we can say that it’s power has been raised by the exponent.

Complete step by step solution:
There is one basic exponential rule that is commonly used everywhere, ${({a^m})^n} = {a^{m \cdot n}}$. Also there is another rule and According to the exponent product rule when multiplying two powers that have the same base, we can add the exponents.
So here we can write the given expression as $\sqrt[4]{{16}}$. We can write $16$ as$2 \times 2 \times 2 \times 2$. It can also be written as in the power form i.e. ${2^4}$.
By putting the values we can write: $\sqrt[4]{{{2^4}}}$. No by applying the formula $\sqrt[n]{{{a^m}}} = {a^{\dfrac{m}{n}}}$ ,
We have: ${2^{\dfrac{4}{4}}} = {2^1}$.

Hence the required answer of the exponential form is $2$.

Note: We know that exponential equations are equations in which variables occurs as exponents. The formula applied before is true for all real values of $m$ and $n$ . We should solve this kind of problem by using the properties of exponents to simplify the problem. We have to keep in mind that if there is a negative value in the power or exponent then it will reverse the number .i.e. ${m^{ - x}}$ will always be equal to $\dfrac{1}{{{m^x}}}$. We should know that the most commonly used exponential function base is the transcendental number which is denoted by $e$.