 # Simplifying Expressions Involving Radicals Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.NKSsqrt{x^{5}}x5 babeeb0oL 2021-01-16 Answered

Simplifying Expressions Involving Radicals Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.  $\sqrt{{x}^{5}}{x}^{5}$

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Step 1
"For any rational exponent in lowest terms, where mm and nn are integers and we define ${a}^{\frac{m}{n}}={\left(\sqrt{n}\left\{a\right\}\right)}^{m}=\sqrt{n}\left\{{a}^{m}\right\}a\frac{m}{n}\left(an\right)m=amn$
If nn is even, then we require that $a\ge 0a\ge 0$"
Step 2
$\sqrt{{x}^{5}}x5$
Consider the given expression,
$\sqrt{{x}^{5}}x5={\left({x}^{5}\right)}^{\frac{1}{2}}\left(x5\right)\frac{1}{2}$
Apply Law of exponents ${a}^{\frac{m}{n}}={\left(\sqrt{n}\left\{a\right\}\right)}^{m}=\sqrt{n}\left\{{a}^{m}\right\}a\frac{m}{n}=\left(an\right)m=amn$ we get,
${\left({x}^{5}\right)}^{\frac{1}{2}}={x}^{\frac{5}{2}}\left({x}^{5}\right)\frac{1}{2}={x}^{52}$
Therefore the expression $\sqrt{{x}^{5}}x5$ simplifies to ${x}^{\frac{5}{2}}{x}^{52}$

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