Question 200348
*[Tex \LARGE 4y^{-\frac{4}{7}}=4\ast\sqrt[7]{y^{-4}}=4\ast\sqrt[7]{\frac{1}{y^{4}}}=\frac{4}{\sqrt[7]{y^{4}}}]


So *[Tex \LARGE 4y^{-\frac{4}{7}}=\frac{4}{\sqrt[7]{y^{4}}}] where *[Tex \LARGE y>0]




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Edit: The next solution is correct in saying that you should rationalize the denominator (forgot all about that...); however, he went about rationalizing the denominator in the wrong way.



To rationalize the denominator of *[Tex \LARGE \frac{4}{\sqrt[7]{y^{4}}}], you need to multiply both the numerator and denominator by 6 copies of *[Tex \LARGE \sqrt[7]{y^{4}}]. This way, you'll end up with



*[Tex \LARGE \frac{4\ast\left(\sqrt[7]{y^{4}}\right)^6}{\left(\sqrt[7]{y^{4}}\right)^7}]



which will simplify to 



*[Tex \LARGE \frac{4\ast\sqrt[7]{y^{3}}}{y}]



So *[Tex \LARGE 4y^{-\frac{4}{7}}= \frac{4\ast\sqrt[7]{y^{3}}}{y}] where *[Tex \LARGE y>0]


Note: I skipped a bunch of steps. Let me know if you need to see them. Also, you can verify your answer by graphing the original expression and the final expression.