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

Dolly Robinson 2020-11-26 Answered
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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Expert Answer

averes8
Answered 2020-11-27 Author has 5719 answers

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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Answered 2021-10-25 Author has 2083 answers

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