 # Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers. sqrt{x^{5}} coexpennan 2021-02-06 Answered
Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers. $\sqrt{{x}^{5}}$
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“For any rational exponent m/n in lowest terms, where m and n are integers and we define.
${a}^{m/n}=\left(\sqrt[n]{a}{\right)}^{m}=\sqrt[n]{{a}^{m}}$
If n is even, then we require that
Calculation:
$\sqrt{{x}^{5}}$
Consider the given expression,
$\sqrt{{x}^{5}}=\left({x}^{5}{\right)}^{\frac{1}{2}}$
Apply Law of exponents ${a}^{m/n}=\left(\sqrt[n]{a}{\right)}^{m}=\sqrt[n]{{a}^{m}}$ we get,
$\left({x}^{5}{\right)}^{1/2}={x}^{\frac{5}{2}}$
Therefore the expression
Final Statement:
The expression