Question

3 by 2 whole square into 2 by 3 whole to the power of minus 4 then the value of x power minus 2

Answer 1

I hope you got your answer

Answer 2

$Given \: \Big(\frac{3}{2}\Big)^{2} \times \Big(\frac{2}{3}\Big)^{-4} = x^{-2}$

$\implies \Big(\frac{2}{3}\Big)^{-2} \times \Big(\frac{2}{3}\Big)^{-4} = x^{-2}$

$\boxed {\pink { Since , \Big(\frac{a}{b}\Big)^{n} = \Big(\frac{b}{a}\Big)^{-n} }}$

$\implies \Big(\frac{2}{3}\Big)^{2+4} = x^{-2}$

$\boxed {\orange { Since , a^{m} \times a^{n} = a^{m +n } }}$

$\implies \Big(\frac{2}{3}\Big)^{-6} = x^{-2}$

$\implies \Big(\frac{2}{3}\Big)^{3\times (-2)} = x^{-2}$

$\implies \Big(\big(\frac{2}{3}\big)^{3}\Big)^{-2} = x^{-2}$

$\implies \Big( \frac{2}{3}\Big)^{3} = x$

$\implies \frac{2^{3}}{3^{3}} = x$

$\implies \frac{8}{27} = x$

Therefore.,

$\red { Value \:of \:x } \green { = \frac{8}{27} }$

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