Question

Find
$find \: ( \frac{p}{q})^{ - 2} \: \: if \: ( \frac{3}{5} )^{ - 6} \times ( \frac{10}{9} ) \: ^{ - 6} = \: ( \frac{p}{q} )^{ - 6}$
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Answer 1

Step-by-step explanation:

${a}^{m} \times {b}^{m} = (ab)^{m} \\ \frac{3}{5} ^{ - 6} \times \frac{10}{9} ^{ - 6} = \frac{p}{q} ^{ - 6} \\ \\ \frac{3 \times 10}{9 \times 5} ^{ - 6} = { \frac{p}{q} }^{ - 6} \\ \\ \frac{2}{3} ^{ - 6} = \frac{p}{q} ^{ - 6} \\ \\ \mathrm{so \: \frac{p}{q} = \frac{2}{3} } \\ \\ { \frac{p}{q} }^{ - 2} = \frac{2}{3} ^{ - 2} = \frac{4}{9} ^{ - 1} \\ \\ \bf{so \: amswer \: is \: \frac{9}{4} }$