Simplify ((40v^2)/(35v^4))÷((20v^3)/(5v))

$\frac{40 v^{2}}{35 v^{4}} \div \frac{20 v^{3}}{5 v}$

To divide by a fraction, multiply by its reciprocal.

$\frac{40 v^{2}}{35 v^{4}} \cdot \frac{5 v}{20 v^{3}}$

Cancel the common factor of $20 v^{2}$ .

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Factor $20 v^{2}$ out of $40 v^{2}$ .

$\frac{20 v^{2} (2)}{35 v^{4}} \cdot \frac{5 v}{20 v^{3}}$

Factor $20 v^{2}$ out of $20 v^{3}$ .

$\frac{20 v^{2} (2)}{35 v^{4}} \cdot \frac{5 v}{20 v^{2} (v)}$

Cancel the common factor.

$\frac{20 v^{2} \cdot 2}{35 v^{4}} \cdot \frac{5 v}{20 v^{2} v}$

Rewrite the expression.

$\frac{2}{35 v^{4}} \cdot \frac{5 v}{v}$

Cancel the common factor of $5 v$ .

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Factor $5 v$ out of $35 v^{4}$ .

$\frac{2}{5 v (7 v^{3})} \cdot \frac{5 v}{v}$

Cancel the common factor.

$\frac{2}{5 v (7 v^{3})} \cdot \frac{5 v}{v}$

Rewrite the expression.

$\frac{2}{7 v^{3}} \cdot \frac{1}{v}$

Multiply $\frac{2}{7 v^{3}}$ and $\frac{1}{v}$ .

$\frac{2}{7 v^{3} v}$

Raise $v$ to the power of $1$ .

$\frac{2}{7 (v^{1} v^{3})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2}{7 v^{1 + 3}}$

Add $1$ and $3$ .

$\frac{2}{7 v^{4}}$

Simplify ((40v^2)/(35v^4))÷((20v^3)/(5v))

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