Question

find x, if
$( \frac{2}{5} )^{ -3} \times ( \frac{2}{5} ) ^{15} = ( \frac{2}{5} ) ^{2 + 3x}$
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Answer 1

Here ,

$( \frac{2}{5}) ^{ - 3} \times ( \frac{2}{5}) ^{15} = ( \frac{2}{5}) ^{2 + 3x} \\ \\ we \: know \: that \: \: \: \: \: \: \: \: \: \: {a}^{m} \times a ^{n} = {a}^{m + n} \\ \\ so \: as \: per \: above \: eqution \: \\ \\ ( \frac{2}{5} ) ^{ - 3 + 15} = ( \frac{2}{5} )^{2 + 3x} \\ \\ ( \frac{2}{5} ) ^{12} = ( \frac{2}{5} ) ^{2 + 3x} \\ \\ now \: we \: compre \: the \: power \: of \: both \: term \: \: \: \: \: \: \: \: \: \: \: \\ we \: get \\ \\ 12 = 2 + 3x \\ \\ 3x = 12 - 2 \\ \\ 3x = 10 \\ \\ x = \frac{10}{3}$

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