Simplify (4a^5)/(7b^4)*(2b^2)/(2a^4)

$\frac{4 a^{5}}{7 b^{4}} \cdot \frac{2 b^{2}}{2 a^{4}}$

Step 1

Combine.

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

Step 2

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 a^{5} (2 b^{2})$ .

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

Cancel the common factors.

Factor $2$ out of $7 b^{4} (2 a^{4})$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $a^{5}$ and $a^{4}$ .

Factor $a^{4}$ out of $2 a^{5} (2 b^{2})$ .

$\frac{a^{4} (2 a (2 b^{2}))}{7 b^{4} (a^{4})}$

Cancel the common factors.

Factor $a^{4}$ out of $7 b^{4} (a^{4})$ .

$\frac{a^{4} (2 a (2 b^{2}))}{a^{4} (7 b^{4})}$

Cancel the common factor.

$\frac{a^{4} (2 a (2 b^{2}))}{a^{4} (7 b^{4})}$

Rewrite the expression.

$\frac{2 a (2 b^{2})}{7 b^{4}}$

Step 4

Cancel the common factor of $b^{2}$ and $b^{4}$ .

Factor $b^{2}$ out of $2 a (2 b^{2})$ .

$\frac{b^{2} (2 a \cdot (2))}{7 b^{4}}$

Cancel the common factors.

Factor $b^{2}$ out of $7 b^{4}$ .

$\frac{b^{2} (2 a \cdot (2))}{b^{2} (7 b^{2})}$

Cancel the common factor.

$\frac{b^{2} (2 a \cdot (2))}{b^{2} (7 b^{2})}$

Rewrite the expression.

$\frac{2 a \cdot (2)}{7 b^{2}}$

Step 5

Multiply $2$ by $2$ .

$\frac{4 a}{7 b^{2}}$