Question

Объясните пожалуйста как решать А10

Answer 1

$a).( \frac{3 {}^{ \frac{1}{2} } \times 3 {}^{ \frac{1}{6} } }{3 {}^{ \frac{1}{3} } }) {}^{ 3} = ( \frac{3 {}^{ \frac{1}{2} + \frac{1}{6} } }{3 {}^{ \frac{1}{3} } } ) {}^{3} = ( \frac{3 {}^{ \frac{2}{3} } }{3 {}^{ \frac{1}{3} } } ) {}^{3} = (3 {}^{ \frac{2}{3} - \frac{1}{3} } ) {}^{3} =( 3 {}^{ \frac{1}{3} } ) {}^{3} = 3 {}^{ \frac{1}{3} \times 3} = {3}^{1} = 3.$

$b).( \frac{2 {}^{ \frac{1}{2} } \times 2 {}^{ \frac{1}{3} } }{2 {}^{ \frac{1}{6} } } ) {}^{3} = ( \frac{2 {}^{ \frac{1}{2} + \frac{1}{3} } }{2 \frac{1}{6} } ) {}^{3} =( \frac{2 {}^{ \frac{5}{6} } }{2 {}^{ \frac{1}{6} } } ) {}^{3} =( 2 {}^{ \frac{5}{6} - \frac{1}{6} } ) {}^{3} = ( {2}^{ \frac{2}{3} } ) {}^{3} = 2 {}^{ \frac{2}{3} \times 3} = {2}^{2} = 4.$