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The expression \(\dfrac{25}{\sqrt[5]{25}}\) equals 5 raised to what power?

 May 16, 2019
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  \(\dfrac{25}{\sqrt[5]{25}}\) ______  
\(=\qquad\) \(\dfrac{25}{25^{\frac15}}\)

 

 

 

 

because   \(\sqrt[n]{x}\,=\,x^\frac1n\)
\(=\qquad\) \(25^{1-\frac15}\)   because   \(\frac{x^a}{x^b}\,=\,x^{a-b}\)
\(=\qquad\) \(25^{\frac45}\)

 

 

 

because   \(1-\frac15\,=\,\frac55-\frac15\,=\,\frac45\)
\(=\qquad\) \((5^2)^{\frac45}\)   because   \(5^2\,=\,25\)
\(=\qquad\) \(5^{2\cdot\frac45}\)

 

 

 

because   \((x^a)^b\,=\,x^{ab}\)
\(=\qquad\) \(5^{\frac85}\)   because   \(2\cdot\frac45\,=\,\frac85\)
.
 May 16, 2019

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