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mathstudent55
Here's a short explanation. Then I'll show you all the steps.

Think of this as a fraction divided by a fraction.
The middle fraction line is the fraction line of the main fraction.
The numerator of the main fraction is a fraction.
The denominator of the main fraction is a fraction.
To divide a fraction by a fraction, multiply the first fraction by the reciprocal of the second fraction.

Here are the steps, shown one by one.

[tex] \dfrac{\frac{7mn^2}{20p^3q}}{\frac{14n^5}{5p^5q^3}} = [/tex]

[tex] = \dfrac{7mn^2}{20p^3q} \div \dfrac{14n^5}{5p^5q^3} [/tex]

[tex] =\dfrac{7mn^2}{20p^3q} \times\dfrac{5p^5q^3}{14n^5} [/tex]

[tex] =\dfrac{7mn^2 \times 5p^5q^3}{20p^3q \times 14n^5} [/tex]

[tex] =\dfrac{35mn^2p^5q^3}{280n^5p^3q} [/tex]

[tex] = \dfrac{mp^2q^2}{8n^3} [/tex]
gmany
[tex]\dfrac{\dfrac{7mn^2}{20p^3q}}{\dfrac{14n^5}{5p^5q^3}}=\dfrac{7mn^2}{20p^3q}\cdot\dfrac{5p^5q^3}{14n^5}= \dfrac{7}{14}\cdot\dfrac{5}{20}\cdot\dfrac{mn^2p^5q^3}{p^3qn^5}\\\\=\dfrac{1}{2}\cdot\dfrac{1}{4}\cdot mn^{2-5}p^{5-3}q^{3-1}=\dfrac{1}{8} mn^{-3}p^2q^2=\dfrac{mp^2q^2}{8n^3}\\\\\text{Used:}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\a^{-n}=\dfrac{1}{a^n} [/tex]

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