Question

$a )\: ( - \frac{7}{3})^{4}$

$b) \: ( \frac{4}{3}) {}^{4} \div ( \frac{4}{3}) {}^{2}$

$c) \: |( - \frac{3}{4}) {}^{3} \div ( - \frac{3}{4}) {}^{5} | {}^{4}$
ayudaa
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Answer 1

Respuesta:

$a )\: ( - \frac{7}{3})^{4}$

$( - \frac{7}{3})^{4} = ( - \frac{{7}^{4} }{ {3}^{4} })$

$( - \frac{{7}^{4} }{ {3}^{4} }) = \frac{2401}{81}$

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$b) \: ( \frac{4}{3}) {}^{4} \div ( \frac{4}{3}) {}^{2}$

$( \frac{4}{3}) {}^{4} \div ( \frac{4}{3}) {}^{2} = ( {\frac{4}{3}})^{4 - 2}$

$( {\frac{4}{3}})^{4 - 2} = ( {\frac{4}{3}})^{2}$

$( {\frac{4}{3}})^{2} = \frac{16}{9}$

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$c) \: |( - \frac{3}{4}) {}^{3} \div ( - \frac{3}{4}) {}^{5} | {}^{4}$

$|( - \frac{3}{4}) {}^{3} \div ( - \frac{3}{4}) {}^{5} | {}^{4} = |( - \frac{3}{4}) ^{ - 2} | ^{4}$

$|( - \frac{3}{4}) ^{ - 2} | ^{4} = (- \frac{3}{4} )^{ - 8}$

$(- \frac{3}{4} )^{ - 8} = - \frac{1}{( \frac{3}{4})^{8} }$

$- \frac{1}{( \frac{3}{4})^{8} } = ( - \frac{4}{3} )^{8}$

$( - \frac{4}{3} )^{8} = \frac{65536}{6561}$