Discussion
If \(5\sqrt{5}\times5^3\div5^{-\frac{3}{2}}=5^{a+2}\), the value of \(a\) is:
Answer: A
\(5^{\frac{3}{2}}\times5^3\div5^{3\frac{3}{2}}=5^{a+2} \)
\(\Rightarrow 5^{\frac{3}{2}}+3+\frac{3}{2}=5^{a+2} \)
\(\Rightarrow \frac{3}{2}+3+\frac{3}{2}=a+2 \)
\(\Rightarrow a+2=6 \)
\(\therefore a=4\)
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