Simplify the expression and express the answer using rational exponents. Assume that all letters denote...

Concept used:
If a is real number n is a positive integer and ${\displaystyle \sqrt[n]{a^m}\text{is a real number then the rational exponent expression}{\displaystyle \sqrt[n]{a^m}\text{is equivalent to radical expression}{\displaystyle a^{\frac{m}{n}}.}}}$
The above statement can be express as,
${\displaystyle \sqrt[n]{a^m}=a^{m\text{/}n}}$
Calculation:
The given expression is ${\displaystyle \sqrt{x^3}.}$
The property of nth ${\displaystyle \sqrt{}}$ is,
${\displaystyle \sqrt[n]{a^m}=a^{m\text{/}n}}$
Substitute 2 for n, 3 for m and x for a in the above equation.
${\displaystyle \sqrt[2]{x^3}={\left(x^{1\text{/}2}\right)}^3}$
${\displaystyle =x^{3\text{/}2}}$
Hence, the solution of the expression ${\displaystyle \sqrt{x^3}is{x}^{3\text{/}2}}$

Answer is given below (on video)