Question 185651
*[Tex \LARGE y^{\frac{3}{7}}\left(y^{-\frac{3}{7}}+7y^{\frac{4}{7}}\right)] ... Start with the given expression.



*[Tex \LARGE y^{\frac{3}{7}}\left(y^{-\frac{3}{7}}\right)+y^{\frac{3}{7}}\left(7y^{\frac{4}{7}}\right)] ... Distribute



*[Tex \LARGE y^{\frac{3}{7}+(-\frac{3}{7})}+7y^{\frac{3}{7}+\frac{4}{7}}] ... Multiply by adding the exponents.



*[Tex \LARGE y^{\frac{3-3}{7}}+7y^{\frac{3+4}{7}}] ... Combine the fractions.



*[Tex \LARGE y^{\frac{0}{7}}+7y^{\frac{7}{7}}] ... Combine like terms.



*[Tex \LARGE y^{0}+7y^{1}] ... Reduce



*[Tex \LARGE 1+7y] ... Simplify




So *[Tex \LARGE y^{\frac{3}{7}}\left(y^{-\frac{3}{7}}+7y^{\frac{4}{7}}\right)=1+7y] where *[Tex \LARGE y \neq 0]