If 5 5 × 5^3 ÷ 5^ - 3/2 = 5^a + 2 , then the value of a is = ?

Answer: Option A

$$\begin{array}{rl}& \text{5}\sqrt{5}\times {\text{5}}^3÷{\text{5}}^{-\frac{3}{2}}\text{ = }{\text{5}}^{a+2}\\ & \Rightarrow {\text{5}}^1\times 5^{\frac{1}{2}}\times {\text{5}}^3÷{\text{5}}^{-\frac{3}{2}}\text{ = }{\text{5}}^{a+2}\\ & \Rightarrow 5^{1+\frac{1}{2}+3-\left(-\frac{3}{2}\right)}=5^{a+2}\\ & \Rightarrow 5^{1+\frac{1}{2}+3+\frac{3}{2}}=5^{a+2}\\ & \Rightarrow 5^6=5^{a+2}\\ & \Rightarrow a+2=6\\ & \Rightarrow a=4\end{array}$$