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$((\frac{a^{6} }{b^{-3}})^{4})^{\frac{1}{12}}=(\frac{a^{6} }{b^{-3}})^{4*\frac{1}{12}}=(\frac{a^{6} }{b^{-3}})^{\frac{1}{3}}=\frac{a^{6*\frac{1}{3}}}{b^{-3*\frac{1}{3}}}=\frac{a^{2}}{b^{-1}}=a^{2}b\\\\Otvet:\boxed {a^{2}b}$

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Maxuch

Чтобы решить, нужны 3 формулы:

1. ${({x}^{a})}^{b} = {x}^{a \times b}$

2. $\frac{1}{ {x}^{ - y} } = {x}^{y}$

3. ${( \frac{x}{y} )}^{n} = \frac{ {x}^{n} }{ {y}^{n} }$

Теперь решим:

$({ {(\frac{ {a}^{6} }{ {b}^{ - 3} }) }^{4} )} ^{ \frac{1}{12} } = {(\frac{ {a}^{6} }{ {b}^{ - 3} } )}^{ \frac{4}{12} } = {(\frac{ {a}^{6} }{ {b}^{ - 3} } )}^{ \frac{1}{3} } = \frac{ {({a}^{6})}^{ \frac{1}{3} } }{ {({b}^{ - 3})}^{ \frac{1}{3} } } = \frac{ {a}^{ \frac{6}{3} } }{ {b}^{ - \frac{3}{3} } } = \frac{ {a}^{2} }{ {b}^{ - 1} } = {a}^{2} \times b$

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