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

May 16, 2019

 $$\dfrac{25}{\sqrt[5]{25}}$$ ______ $$=\qquad$$ $$\dfrac{25}{25^{\frac15}}$$ 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   $$2\cdot\frac45\,=\,\frac85$$