Question
Find x.
$-\frac{2}{5}^{2\text{x}+6}\times\frac{2}{5}^{3}=\frac{2}{5}^{\text{x+2}}$
$-\frac{2}{5}^{2\text{x}+6}\times\frac{2}{5}^{3}=\frac{2}{5}^{\text{x+2}}$
✓
Answer
We have, $\frac{2}{5}^{2\text{x}+6}\times\frac{2}{5}^{3}=\frac{2}{5}^{\text{x+2}}$
Using law of exponents, $a^m \times a^n=(a)^{m+n}$ $[\because$ a is non-zero integer$]$
Then, $\Big(\frac{2}{5}\Big)^{2\text{x}+6+3}=\Big(\frac{2}{5}\Big)^{\text{x+2}}$
On compairing powers of $\big(\frac{2}{5}\big)$, we get.
$2x + 6 + 3 = x + 2 $
$⇒ 2x + 9 = x + 2 $
$⇒ x = -7$
Using law of exponents, $a^m \times a^n=(a)^{m+n}$ $[\because$ a is non-zero integer$]$
Then, $\Big(\frac{2}{5}\Big)^{2\text{x}+6+3}=\Big(\frac{2}{5}\Big)^{\text{x+2}}$
On compairing powers of $\big(\frac{2}{5}\big)$, we get.
$2x + 6 + 3 = x + 2 $
$⇒ 2x + 9 = x + 2 $
$⇒ x = -7$
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