Question

$\frac{\left(m+\left(mn^2\right)^{\frac{1}{3}}+\left(m^2n\right)^{\frac{1}{3}}\right)}{m-n}\cdot \left(1-\frac{n^{\frac{1}{3}}}{m^{\frac{1}{3}}}\right)$

Answer 1

Answer:

1.

Step-by-step explanation:

$\frac{(m + {(m {n}^{2} )}^{ \frac{1}{3} } + {{(m}^{2}n)}^{ \frac{1}{3} } )}{m - n} \times (1 - \frac{ {n}^{ \frac{1}{3} } }{ {m}^{ \frac{1}{3} } } ) \\ = \frac{(m + {m}^{ \frac{1}{3}} {n}^{ \frac{2}{3} } + {m}^{ \frac{2}{3} } {n}^{ \frac{1}{3} } ) }{m - n} \times \frac{( {m }^{ \frac{1}{3} } - {n}^{ \frac{1}{3} } )}{ {m}^{ \frac{1}{3} } } \\ = (\frac{m}{ {m}^{ \frac{1}{3} } } + \frac{ {m}^{ \frac{1}{3} } {n}^{ \frac{2}{3} } }{ {m}^{ \frac{1}{3} } } + \frac{ {m}^{ \frac{2}{3} } {n}^{ \frac{1}{3} } }{ {m}^{ \frac{1}{3} } } ) \times \frac{( {m}^{ \frac{1}{3} } - {n}^{ \frac{1}{3} } )}{m - n} \\ = ( {m}^{ \frac{2}{3} } + {n}^{ \frac{2}{3} } + {m}^{ \frac{1}{3} }{n}^{ \frac{1}{3} } ) \times \frac{ {m}^{ \frac{1}{3} } - {n}^{ \frac{1}{3} } }{m - n} \\ = \frac{m - n - {m}^{ \frac{2}{3} } {n}^{ \frac{ 1 }{3} } + {m}^{ \frac{1}{3} } {n}^{ \frac{2}{3} } + {m}^{ \frac{2}{3} } {n}^{ \frac{1}{3} } - {m}^{ \frac{1}{3} } {n}^{ \frac{2}{3} } }{m - n} \\ = \frac{m - n}{m - n} \\ = 1$