Question

Simplifique as potências abaixo:

Answer 1

$c) \: {( {a}^{3} )}^{3} \times {a}^{ - 2} = \\ {a}^{3 \times 3} \times {a}^{ - 2} = \\ {a}^{9} \times {a}^{ - 2} = \\ {a}^{9 + ( - 2)} = \\ {a}^{7}$
$f)( \frac{1}{2} )^{4} \times ( \frac{2}{3} )^{3} \times ( \frac{1}{3} )^{ - 2} = \\ {2}^{ - 4} \times \frac{ {2}^{3} }{ {3}^{3} } \times {3}^{2} = \\ \frac{ {2}^{ - 4} \times {2}^{3} }{ {3}^{3} } \times {3}^{2} = \\ \frac{ {2}^{ - 4 + 3} }{ {3}^{3} } \times {3}^{2} = \\ \frac{ {2}^{ - 1} \times {3}^{2} }{ {3}^{3} } = \\ {2}^{ - 1} \times \frac{ {3}^{2} }{ {3}^{3} } = \\ {2}^{ - 1} \times {3}^{2 - 3} = \\ {2}^{ - 1} \times {3}^{ - 1} = \\ {(2 \times 3)}^{ - 1} = \\ {6}^{ - 1} = \frac{1}{6}$
Espero ter ajudado.

$d) \: \frac{ {11}^{2} \times {11}^{4} }{11^{3} } = \\ \frac{{11}^{6}}{ {11}^{3} } = \\ {11}^{6 - 3} = \\ {11}^{3}$
$e) \: {(3a)}^{2} \times { (\frac{a}{3} )}^{2} = \\ (3a \times \frac{a}{3} )^{2} = \\ ( \frac{ 3{a}^{2} }{3} )^{2} = \\ { ({a}^{2} )}^{2} = \\ {a}^{4}$