If \(5 \sqrt{5} \times 5^{3} \div 5^{-3 / 2}=5^{(a+2)}\), then value of \(a\) is

Given the equation:

\[
5 \sqrt{5} \times 5^3 \div 5^{-3 / 2} = 5^{(a+2)}
\]

We start by expressing all terms as powers of 5:

\[
5^1 \times 5^{\frac{1}{2}} \times 5^3 \div 5^{-\frac{3}{2}} = 5^{a+2}
\]

When you combine the exponents, you add them:

\[
5^{1 + \frac{1}{2} + 3} \times 5^{\frac{3}{2}} = 5^{a+2}
\]

Since multiplying with the same base allows you to add exponents:

\[
5^{\frac{2}{2} + \frac{1}{2} + \frac{6}{2} + \frac{3}{2}} = 5^{a+2}
\]

Simplify the exponents:

\[
5^{\frac{12}{2}} = 5^{a+2}
\]

Which simplifies further to:

\[
5^6 = 5^{a+2}
\]

Setting the exponents equal to each other gives us:

\[
a+2 = 6
\]

Solving for \(a\):

\[
a = 6 – 2
\]
\[
a = 4
\]

Therefore, the value of \(a\) is \(\boldsymbol{4}\).