[tex]\sqrt[3]{\frac{y^{2} }{y^{\frac{4}{5} } } } = y^{\frac{2}{5} }[/tex]
How to rewrite an expression?
Rewriting an expression might be to simplify the expression or to rewrite the expression with the minimal number of items and values.
But we were asked to rewrite the expression to the form yⁿ.
Therefore,
[tex]\sqrt[3]{\frac{y^{2} }{y^{\frac{4}{5} } } }[/tex]
Hence,
[tex]\sqrt[3]{\frac{y^{2} }{y^{\frac{4}{5} } } } = \sqrt[3]{y^{2-\frac{4}{5} } }[/tex]
Therefore, let's subtract the powers
[tex]\sqrt[3]{\frac{y^{2} }{y^{\frac{4}{5} } } } = \sqrt[3]{y^{2-\frac{4}{5} } } = \sqrt[3]{y^{\frac{10-4}{5} } }[/tex]
[tex]\sqrt[3]{\frac{y^{2} }{y^{\frac{4}{5} } } } = \sqrt[3]{y^{2-\frac{4}{5} } } = \sqrt[3]{y^{\frac{10-4}{5} } } = \sqrt[3]{y^{\frac{6}{5} } }[/tex]
Using law of indices,
[tex]\sqrt[3]{\frac{y^{2} }{y^{\frac{4}{5} } } } = \sqrt[3]{y^{2-\frac{4}{5} } } = \sqrt[3]{y^{\frac{10-4}{5} } } = \sqrt[3]{y^{\frac{6}{5} } } = y^{\frac{6}{5}(\frac{1}{3} ) }[/tex]
Finally,
[tex]\sqrt[3]{\frac{y^{2} }{y^{\frac{4}{5} } } } = y^{\frac{6}{5}(\frac{1}{3} ) } = y^{\frac{2}{5} }[/tex]
learn more on expression here: h7ttps://brainly.com/question/1379643
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