Question
Evaluate :${\left( {\frac{5}{8}} \right)^{ - 7}} \times {\left( {\frac{8}{5}} \right)^{ - 4}}$
✓
Answer
${\left( {\frac{5}{8}} \right)^{ - 7}} \times {\left( {\frac{8}{5}} \right)^{ - 4}}$
$ = \frac{{{5^{ - 7}}}}{{{8^{ - 7}}}} \times \frac{{{8^{ - 4}}}}{{{5^{ - 4}}}}$
$ = \frac{{{5^{ - 7}}}}{{{5^{ - 4}}}} \times \frac{{{8^{ - 4}}}}{{{8^{ - 7}}}}$
$ =5^{(-7)-(-4)} \times 8^{(-4)-(-7)} $
$ =5^{-7+4} \times 8^{-4+7} $
$ =5^{-3} \times 8^3 $
$\frac{1}{{{5^3}}} \times {8^3}$
$ = \frac{{{8^3}}}{{{5^3}}}$
$ = \frac{{512}}{{125}}$$ = 4\frac{{12}}{{125}}$
$ = \frac{{{5^{ - 7}}}}{{{8^{ - 7}}}} \times \frac{{{8^{ - 4}}}}{{{5^{ - 4}}}}$
$ = \frac{{{5^{ - 7}}}}{{{5^{ - 4}}}} \times \frac{{{8^{ - 4}}}}{{{8^{ - 7}}}}$
$ =5^{(-7)-(-4)} \times 8^{(-4)-(-7)} $
$ =5^{-7+4} \times 8^{-4+7} $
$ =5^{-3} \times 8^3 $
$\frac{1}{{{5^3}}} \times {8^3}$
$ = \frac{{{8^3}}}{{{5^3}}}$
$ = \frac{{512}}{{125}}$$ = 4\frac{{12}}{{125}}$
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