# Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers. displaystylesqrt{{{x}^{3}}}

Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
$$\displaystyle\sqrt{{{x}^{3}}}$$

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averes8

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 $$\displaystyle\sqrt{{{x}^{3}}}\ {i}{s}\ {x}^{{{3}\text{/}{2}}}$$

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content_user

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