Question

simplify and write in exponential form (81/16)^-1/2 * (2/3)^2 + (3/2)^-2

Answer 1

Hi friends

Here is your answer

$( \frac{81}{16} ) {}^{ \frac{ - 1}{2} } \times ( \frac{2}{3} ) {}^{2} + ( \frac{3}{2} ) {}^{ - 2} \\ \\ = ( \frac{16}{81}) {}^{ \frac{1}{2} } \times \frac{4}{3} + ( \frac{2}{3} ) {}^{2} \\ \\ = \frac{4}{9} \times \frac{4}{3} + \frac{4}{9} \\ \\ = \frac{4}{9} ( \frac{4}{3} + 1) \\ \\ = \frac{4}{9} ( \frac{4 + 3}{3} ) \\ \\ = \frac{4}{9} \times \frac{7}{3} \\ \\ = \frac{28}{27}$
Hope it helps you

Thanks
@MSD

Answer 2

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Here is your answer.
$( \frac{81}{16} ) {}^{ \frac{ - 1}{2} } \times( \frac{2}{3}) {}^{2} + ( \frac{3}{2} ) {}^{ - 2} \\ \\ = ( \frac{16}{81} ) {}^{ \frac{1}{2} } \times \frac{4}{9} + ( \frac{2}{3} ) {}^{2} \\ \\ = \frac{4}{9} \times \frac{4}{9} + \frac{4}{9} \\ \\ = \frac{4}{9} ( \frac{4}{9} + 1) \\ \\ = \frac{4}{9} ( \frac{4 + 9}{9} ) \\ \\ = \frac{4}{9} \times \frac{13}{9} \\ \\ = \frac{52}{81} \\ or \: in \: exponention \: form \\ \\ = {2}^{2} \times 13 {}^{1} \times {3}^{ - 4}$
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