Question

If $5\sqrt{5}\times 5^3÷5^{-\frac{3}{2}}=5^{a+2}$ then the value of $a$ is:

• A. $4$
• B. $5$
• C. $6$
• D. $8$

Answer 1

Answer: (A)

$4$

$5\sqrt{5}\times 5^3÷5^{-\frac{3}{2}}=5^{a+2}$

$\Rightarrow \frac{5\sqrt{5}\times 5^3}{5^{-\frac{3}{2}}}=5^{a+2}$

$\Rightarrow \frac{5^3\times 5^{\frac{3}{2}}}{5^{-\frac{3}{2}}}=5^{a+2}$

$\Rightarrow 5^{3+\frac{3}{2}-(-\frac{3}{2})}=5^{a+2}$

$\Rightarrow 5^{3+\frac{3}{2}+\frac{3}{2}}=5^{a+2}$

$\Rightarrow 5^6=5^{a+2}$

Base are same so

$\Rightarrow 6=a+2\Rightarrow a=4$