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Power of a Power

Simplify 5√...

Question

Simplify $5 \sqrt{5} \times 5^{3} \div 5^{- 3 / 2}$

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Solution

$5 \sqrt{5} \times 5^{3} \div 5^{\frac{- 3}{2}} =$
LHS:
$5^{4} \sqrt{5} \div (\sqrt{5})^{2} \times (\frac{- 3}{2})$
$= 625 \sqrt{5} \div \frac{1}{5 \sqrt{5}}$
$= 625 \sqrt{5} \times \frac{5 \sqrt{5}}{1}$
$= 625 \times 5 \times 5$
$= 625 \times 25$
$= 15625$

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