Question

the question must be solved in the whole process system know step must be missed

Answer 1

Hope every step is included... And it must be right...

Answer 2

Hello............. ^_^

Here is your answer....

${9}^{x} \times {3}^{2} \times { [{3}^{ \frac{ - x}{2} }] }^{ - 2} \: \: = \frac{1}{27} \: \: find \: \: value \: \: of \: x \\ \\ 9 = {3}^{2} \\ 27 = {3}^{3 } \\ \\ = > ({3})^{2x} \times {3}^{2} \times {(3)}^{ \frac{ - x}{2} \times - 2} \: \: \: = \frac{1}{ {(3)}^{3} } \\ \\ = > {(3)}^{2x} \times {3}^{2} \times {(3)}^{x} \: \: \: = {(3)}^{ - 3} \\ \\ = > {(3)}^{2x + 2 + x} \: \: \: = {(3)}^{ - 3} \\ \\ = > ({3)}^{3x + 2} \: \: \: = {(3)}^{ - 3} \\ \\ now \: \: bases \: \: are \: \: same \\now \: equating \: their \: powers\\ \\ = > 3x + 2 \: = - 3 \\ \\ = > 3x + = - 3 - 2 \\ \\ = > 3x = - 5 \\ \\ = > x = \frac{ - 5}{3}$
$so \: \: value \: \: of \: x \: = \frac{ - 5}{3}$




CHECK

${9}^{x} \times {3}^{2} \times { [ {3}^{ \frac{ - x}{2} } ]}^{ - 2} \\ \\ = ({3)}^{2x} \times {3}^{2} \times {(3)}^{ \frac{ - x}{2} \times - 2} \\ \\ = {(3)}^{2x} \times {3}^{2} \times {(3)}^{x} \\ \\ = {(3})^{2 \times \frac{ - 5}{3} } \times {3}^{2} \times {(3)}^{ \frac{ - 5}{3} } \\ \\ = {(3)}^{ \frac{ - 10}{3} + 2 + \frac{ - 5}{3} } \\ \\ = {(3)}^{ \frac{ - 10 + 6 - 5}{3} } \\ \\ = {(3)}^{ \frac{ - 15 + 6}{3} } \\ \\ = {(3)}^{ \frac{ - 9}{3} } \\ \\ = {(3)}^{ - 3} = \frac{1}{ {(3)}^{ 3} } = \frac{1}{27}$

Hope it helps................. ^_^