Question

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

• A. $-1$
• B. $0$
• C. $-2$
• D. $2$

Answer 1

The correct option is C $-2$

Given, ${\left(\frac{3}{2}\right)}^2\times {\left(\frac{3}{2}\right)}^{a+5}={\left(\frac{3}{2}\right)}^5$

It can be written as,

${\left(\frac{3}{2}\right)}^{(2+a+5)}={\left(\frac{3}{2}\right)}^5$

Comparing powers on both sides,

$\Rightarrow a+7=5$

$\Rightarrow a=-2$