Question

If ${\left(\frac{3}{2}\right)}^2\times {\left(\frac{3}{2}\right)}^{a+5}={\left(\frac{3}{2}\right)}^8$, then the value of $a$ is:

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

The correct option is C $1$

${\left(\frac{3}{2}\right)}^2\times {\left(\frac{3}{2}\right)}^{a+5}={\left(\frac{3}{2}\right)}^8$
$\Rightarrow {\left(\frac{3}{2}\right)}^{a+7}={\left(\frac{3}{2}\right)}^8$
$\Rightarrow a+7=8$
$\Rightarrow a=8-7=1$