Question

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

• A. 4
• B. 5
• C. 6
• D. 8
• E. 7

Answer 1

The correct option is A

4

$\begin{array}{cc}\frac{5\sqrt{5}\times 5^3}{5^{-3/2}}=5^{a+2}\Rightarrow \frac{5^{3/2}\times 5^3}{5^{-3/2}}=5^{a+2}& \\ \Rightarrow 5^{\left(\frac{3}{2}+3+\frac{3}{2}\right)}=5^{a+2}\Rightarrow 5^6=5^{a+2}& \\ \Rightarrow 6=a+2& \therefore a=4.\end{array}$