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  • 14-12-2018
  • Mathematics
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Rewrite the rational exponent as a radical.


(5*3/4 power)2/3 power

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gmany
gmany gmany
  • 14-12-2018

[tex]Use:\\\sqrt[n]{a^m}=a^{\frac{m}{n}}\\\\(a^n)^m=a^{nm}\\\\\left(5^{\frac{3}{4}}\right)^{\frac{2}{3}}=5^{\frac{3}{4}\cdot\frac{2}{3}}=5^{\frac{1}{2}\cdot\frac{1}{1}}=5^{\frac{1}{2}}=\sqrt[2]{5}=\boxed{\sqrt5}[/tex]

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