Simplify (66a^2b^2)/21*(7b^3)/(3a^4)

$\frac{66 a^{2} b^{2}}{21} \cdot \frac{7 b^{3}}{3 a^{4}}$

Combine.

$\frac{66 a^{2} b^{2} (7 b^{3})}{21 (3 a^{4})}$

Multiply $b^{2}$ by $b^{3}$ by adding the exponents.

Move $b^{3}$ .

$\frac{66 a^{2} (b^{3} b^{2}) \cdot 7}{21 (3 a^{4})}$

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

$\frac{66 a^{2} b^{3 + 2} \cdot 7}{21 (3 a^{4})}$

Add $3$ and $2$ .

$\frac{66 a^{2} b^{5} \cdot 7}{21 (3 a^{4})}$

Cancel the common factor of $66$ and $21$ .

Factor $3$ out of $66 a^{2} b^{5} \cdot 7$ .

$\frac{3 (22 a^{2} b^{5} \cdot 7)}{21 (3 a^{4})}$

Cancel the common factors.

Factor $3$ out of $21 (3 a^{4})$ .

$\frac{3 (22 a^{2} b^{5} \cdot 7)}{3 (7 (3 a^{4}))}$

Cancel the common factor.

$\frac{3 (22 a^{2} b^{5} \cdot 7)}{3 (7 (3 a^{4}))}$

Rewrite the expression.

$\frac{22 a^{2} b^{5} \cdot 7}{7 (3 a^{4})}$

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

Factor $a^{2}$ out of $22 a^{2} b^{5} \cdot 7$ .

$\frac{a^{2} (22 b^{5} \cdot 7)}{7 (3 a^{4})}$

Cancel the common factors.

Factor $a^{2}$ out of $7 (3 a^{4})$ .

$\frac{a^{2} (22 b^{5} \cdot 7)}{a^{2} (7 (3 a^{2}))}$

Cancel the common factor.

$\frac{a^{2} (22 b^{5} \cdot 7)}{a^{2} (7 (3 a^{2}))}$

Rewrite the expression.

$\frac{22 b^{5} \cdot 7}{7 (3 a^{2})}$

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{22 b^{5} \cdot 7}{7 (3 a^{2})}$

Rewrite the expression.

$\frac{22 b^{5}}{3 a^{2}}$