Question

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Answer 1

Answer:

$( \frac{2}{5} ) {}^{2x + 6} \times ( \frac{2}{5} ) {}^{3} = ( \frac{2}{5} ) {}^{x + 2} \\ apply \: a {}^{m} \times a {}^{n} = a {}^{m + n} \: to \: the \: left\:side\: of\:equation \\ = ( \frac{2}{5} ) {}^{2x + 6 + 3} = ( \frac{2}{5} ) {}^{x + 2} \\ = ( \frac{2}{5} ) {}^{2x + 9} = ( \frac{2}{5} ) {}^{x + 2} \\ now \: apply \: formula \\ a {}^{n} = a {}^{m} \\ = n = m \\ so \: 2x + 9 = x + 2 \\ = 2x + 9 - x - 2 = 0 \\ = x + 7 = 0 \\ = x = - 7 \: \: answer$

Answer 2

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Question}}}}}}}}$

Find the value of x

$\sf(\dfrac{2}{5})^{2x+6} \times(\dfrac{2}{5})^{2} = (\dfrac{2}{5})^{x+2}$

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Solution}}}}}}}}$

$\sf\implies(\dfrac{2}{5})^{2x+6} \times(\dfrac{2}{5})^2= (\dfrac{2}{5})^{x+2}$

$x^a \times x^b = x^{a+b}$

$\sf\implies(\dfrac{2}{5})^{2x+6+3} = (\dfrac{2}{5})^{x+2}$

$\sf\implies(\dfrac{4}{9})^{2x+9} = (\dfrac{4}{9})^{x+2}$

when bases are equal then power will also be equal

$\sf\implies 2x+9 = x+2$

$\sf\implies 2x - x = 2-9$

$\sf\implies x = -7$

${\bold{\blue{\boxed{\bf{x = -7 }}}}}$

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