Question

(81/16)-1/2 * (2/3)2 ÷(3/2)-2

Answer 1

Hey friend,
Here is the answer you were looking for:
$( \frac{81}{16} )^{ - \frac{1}{2} } \times {( \frac{2}{3}) }^{2} \div {( \frac{3}{2}) }^{ - 2} \\ \\ using \: th \: identity \\ {( \frac{a}{b}) }^{ - m} = {( \frac{b}{a}) }^{m} \\ \\ = {( \frac{16}{81}) }^{ \frac{1}{2} } \times {( \frac{2}{3} )}^{2} \div {( \frac{2}{3}) }^{2} \\ \\ = {( \frac{16}{81} )}^{ \frac{1}{2} } \times {( \frac{2}{3} )}^{2} \times {( \frac{3}{2}) }^{2} \\ \\ splitting \: we \: get \\ \\ = \frac{ {4}^{2 \times \frac{1}{2} } }{ {9}^{2 \times \frac{1}{2} } } \times \frac{ {2}^{2} }{ {3}^{2} } \times \frac{ {3}^{2} }{ {2}^{2} } \\ \\ = \frac{4}{9} \times \frac{2 \times 2}{3 \times 3} \times \frac{3 \times 3}{2 \times 2} \\ \\ = \frac{4}{9}$

Hope this helps!!

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@Mahak24

Thanks...
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