How do you simplify (5 times q ^3) /sqrtq^11?

Feb 15, 2016

$\frac{5 \sqrt{q}}{q} ^ 3 \text{ but "5q^(-5/2)" is better!}$

Explanation:

Assumption: You meant the question to look like

$\frac{5 \times {q}^{3}}{\sqrt{{q}^{11} \textcolor{w h i t e}{.}}}$

Write as $\text{ } 5 \times \frac{{q}^{3}}{{q}^{\frac{11}{2}}}$

$\implies 5 \times {q}^{\frac{6}{2} - \frac{11}{2}} \text{ "=" } 5 {q}^{- \frac{5}{2}}$

$\implies \frac{5}{\sqrt{{q}^{5}}}$

=>5/(sqrt(q^2xxq^2xxqcolor(white)(.))

$\implies \frac{5}{{q}^{2} \sqrt{q}}$

Not good practice to have a root as a denominator
So multiply by but in the form of $\frac{\sqrt{q}}{\sqrt{q}}$

Giving

$\frac{5 \sqrt{q}}{q} ^ 3 \text{ or just use the earlier value of } 5 {q}^{- \frac{5}{2}}$