Question

If ${\left(\frac{3}{2}\right)}^2\times {\left(\frac{3}{2}\right)}^{a+5}={\left(\frac{3}{2}\right)}^8$, then $a=$______ .

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

Answer: (C)

$1$

${\left(\frac{3}{2}\right)}^2\times {\left(\frac{3}{2}\right)}^{a+5}={\left(\frac{3}{2}\right)}^8\Rightarrow {\left(\frac{3}{2}\right)}^{a+7}={\left(\frac{3}{2}\right)}^8$
On comparing, we get, $a+7=8\Rightarrow a=1$