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Powers with Negative Exponents

Simplify1/6 |...

Question

Simplify
${\frac{1}{6^{(- 2)}} - \frac{1}{3^{(- 3)}}} \div \frac{1}{5^{(- 2)}}$

A

$(\frac{3}{5})^{2}$

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B

$(\frac{9}{25})^{2}$

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C

$(\frac{5}{3})^{2}$

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D

$(\frac{25}{9})^{2}$

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Solution

The correct option is A
$(\frac{3}{5})^{2}$

${\frac{1}{6^{(- 2)}} - \frac{1}{3^{(- 3)}}}$ ÷ $\frac{1}{5^{(- 2)}}$
$\Rightarrow$ ${36 - 27} \times \frac{1}{25}$
$\Rightarrow$ $9 \times \frac{1}{25}$
$\Rightarrow$ $\frac{9}{25} = (\frac{3}{5})^{2}$

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\frac{3^{5} \times 3^{9}}{12}

{[\frac{- 1 + i \sqrt{3}}{2}]}^{6} + {[\frac{- 1 - i \sqrt{3}}{2}]}^{6} + {[\frac{- 1 + i \sqrt{3}}{2}]}^{5} + {[\frac{- 1 - i \sqrt{3}}{2}]}^{5} =

{[\frac{- 1 + i \sqrt{3}}{2}]}^{6} + {[\frac{- 1 - i \sqrt{3}}{2}]}^{6} + {[\frac{- 1 + i \sqrt{3}}{2}]}^{5} + {[\frac{- 1 - i \sqrt{3}}{2}]}^{5} =

Using appropriate properties, find:

i) $- \frac{2}{3} \times \frac{3}{5} + \frac{5}{2} - \frac{3}{5} \times \frac{1}{6}$

\frac{2}{5} \times (\begin{matrix} - \frac{3}{7} \end{matrix}) - \frac{1}{6} \times \frac{3}{2} + \frac{1}{14} \times \frac{2}{5}

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