 # Use rational exponents to simplify. Write the answer in radical notation if appropriate (sqrt{cd})^{14} mattgondek4 2020-12-17 Answered
Use rational exponents to simplify. Write the answer in radical notation if appropriate $\left(\sqrt{cd}{\right)}^{14}$
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Given:
$\left(\sqrt{cd}{\right)}^{14}$
We need use property of rational exponents
$\left(\sqrt[b]{a}{\right)}^{c}={\left(\frac{\left(a{\right)}^{1}}{b}\right)}^{c}=\left({a}^{\frac{c}{b}}\right)$
use property of rational exponents
$\left(\sqrt[b]{a}{\right)}^{c}={\left(\frac{\left(a{\right)}^{1}}{b}\right)}^{c}=\left({a}^{\frac{c}{b}}\right)$
${\left(\frac{\left(CD{\right)}^{1}}{7}\right)}^{14}=\frac{\left(CD{\right)}^{14}}{7}=\left(CD{\right)}^{2}={C}^{2}{D}^{2}$
Finally answer is: $\left(CD{\right)}^{2}={C}^{2}{D}^{2}$
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