Question

simplify.
\frac{\frac{15n^{5}}{7p^{4}q^{2}}}{\frac{5mn^{3}}{14p^{2}q}}

Explanation:

Step1: Rewrite as multiplication of reciprocals

Dividing by a fraction is multiplying by its reciprocal. So we have:
$$\frac{15n^{5}}{7p^{4}q^{2}} \div \frac{5mn^{3}}{14p^{2}q} = \frac{15n^{5}}{7p^{4}q^{2}} \times \frac{14p^{2}q}{5mn^{3}}$$

Step2: Simplify coefficients and variables separately

For coefficients: $\frac{15\times14}{7\times5}=\frac{210}{35} = 6$
For $n$: $\frac{n^{5}}{n^{3}}=n^{5 - 3}=n^{2}$
For $p$: $\frac{p^{2}}{p^{4}}=p^{2-4}=p^{-2}=\frac{1}{p^{2}}$
For $q$: $\frac{q}{q^{2}}=q^{1 - 2}=q^{-1}=\frac{1}{q}$
For $m$: There is only one $m$ in the denominator, so it remains as $\frac{1}{m}$

Step3: Combine all simplified parts

Multiply the simplified coefficients and variables together:
$6\times n^{2}\times\frac{1}{p^{2}}\times\frac{1}{q}\times\frac{1}{m}=\frac{6n^{2}}{mp^{2}q}$

Answer:

$\frac{6n^{2}}{mp^{2}q}$