# To write: An expression using rational exponents and using radicals. 5x^{frac{5}{2}}+2x^{frac{1}{2}}+x^{frac{3}{2}}

To write: An expression using rational exponents and using radicals.
$5{x}^{\frac{5}{2}}+2{x}^{\frac{1}{2}}+{x}^{\frac{3}{2}}$
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casincal
An expression in rational exponents is as follows:
$5{x}^{\frac{5}{2}}+2{x}^{\frac{1}{2}}+{x}^{\frac{3}{2}}$
Now the above expression can be written as
$5{\left({x}^{5}\right)}^{\frac{1}{2}}+2\sqrt{x}+{\left({x}^{3}\right)}^{\frac{1}{2}}$
$⇒5\sqrt{{x}^{5}}+2\sqrt{x}+\sqrt{{x}^{3}}$
This is the required expression in radical form.
Jeffrey Jordon