The expression \(\dfrac{25}{\sqrt[5]{25}}\) equals 5 raised to what power?
+9466 | \(\dfrac{25}{\sqrt[5]{25}}\) | ______ | ||
| \(=\qquad\) | \(\dfrac{25}{25^{\frac15}}\) |
| 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 \(2\cdot\frac45\,=\,\frac85\) |
