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

Guest May 16, 2019

1⁺⁰ Answers

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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 $2\cdot\frac45\,=\,\frac85$

hectictar May 16, 2019

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