[4] If 5\sqrt{5}\times 5^{3}+5^{-\dfrac{3}{2}} =5^{a+2}, then the value of a is:

For Competitive Exams

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

Explanation:

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

$\Leftrightarrow \dfrac{5 \times 5^{\dfrac{1}{2}} \times 5^{3}}{5^{-\dfrac{3}{2}}}=5^{a+2}$

$\Leftrightarrow 5^{\left(1+\dfrac{1}{2}+3+\dfrac{3}{2}\right)}$ $=5^{a+2}$

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

$\Leftrightarrow a+2=6$

$\Leftrightarrow a=4$

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