Write the Fraction in Simplest Form (20v^9)/((4v)^2)

$\frac{20 v^{9}}{{(4 v)}^{2}}$

Simplify the denominator.

Apply the product rule to $4 v$ .

$\frac{20 v^{9}}{4^{2} v^{2}}$

Raise $4$ to the power of $2$ .

$\frac{20 v^{9}}{16 v^{2}}$

$\frac{20 v^{9}}{16 v^{2}}$

Cancel the common factor of $20$ and $16$ .

Factor $4$ out of $20 v^{9}$ .

$\frac{4 (5 v^{9})}{16 v^{2}}$

Cancel the common factors.

Factor $4$ out of $16 v^{2}$ .

$\frac{4 (5 v^{9})}{4 (4 v^{2})}$

Cancel the common factor.

$\frac{4 (5 v^{9})}{4 (4 v^{2})}$

Rewrite the expression.

$\frac{5 v^{9}}{4 v^{2}}$

$\frac{5 v^{9}}{4 v^{2}}$

$\frac{5 v^{9}}{4 v^{2}}$

Cancel the common factor of $v^{9}$ and $v^{2}$ .

Factor $v^{2}$ out of $5 v^{9}$ .

$\frac{v^{2} (5 v^{7})}{4 v^{2}}$

Cancel the common factors.

Factor $v^{2}$ out of $4 v^{2}$ .

$\frac{v^{2} (5 v^{7})}{v^{2} \cdot 4}$

Cancel the common factor.

$\frac{v^{2} (5 v^{7})}{v^{2} \cdot 4}$

Rewrite the expression.

$\frac{5 v^{7}}{4}$

$\frac{5 v^{7}}{4}$

$\frac{5 v^{7}}{4}$

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