To simplify: The given expression sqrt{x^{3}}

To simplify:
The given expression $\sqrt{{x}^{3}}$
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Step 1
Law of exponents:
For any rational exponent $\frac{m}{n}$ in lowest terms, where m and n are integers and $n>0,$ we define
${a}^{\frac{m}{n}}={\left(\sqrt{n}\left\{a\right\}\right)}^{m}=\sqrt{n}\left\{{a}^{m}\right\}$
If n is even, then we require that $a\ge 0$
Step 2
Consider the given expression,
$\sqrt{{x}^{3}}={\left({x}^{3}\right)}^{\frac{1}{2}}$
Apply Law of exponents ${a}^{\frac{m}{n}}={\left(\sqrt{n}\left\{a\right\}\right)}^{m}=\sqrt{n}\left\{{a}^{m}\right\}$ we get,
${\left({x}^{3}\right)}^{\frac{1}{2}}={x}^{\frac{3}{2}}$
Therefore the expression $\sqrt{{x}^{3}}$ simplifies to ${x}^{\frac{3}{2}}$
Final Statement:
The simplified form of $\sqrt{{x}^{3}}$ is ${x}^{\frac{3}{2}}$