Simplify (-12xy)/(7y^4)*(21x^5y^2)/(4y)

$\frac{- 12 x y}{7 y^{4}} \cdot \frac{21 x^{5} y^{2}}{4 y}$

Combine.

$\frac{- 12 x y (21 x^{5} y^{2})}{7 y^{4} (4 y)}$

Multiply $x$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$\frac{- 12 (x^{5} x) y (21 y^{2})}{7 y^{4} (4 y)}$

Multiply $x^{5}$ by $x$ .

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

$\frac{- 12 (x^{5} x^{1}) y (21 y^{2})}{7 y^{4} (4 y)}$

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

$\frac{- 12 x^{5 + 1} y (21 y^{2})}{7 y^{4} (4 y)}$

Add $5$ and $1$ .

$\frac{- 12 x^{6} y (21 y^{2})}{7 y^{4} (4 y)}$

Multiply $y$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$\frac{- 12 x^{6} (y^{2} y) \cdot 21}{7 y^{4} (4 y)}$

Multiply $y^{2}$ by $y$ .

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

$\frac{- 12 x^{6} (y^{2} y^{1}) \cdot 21}{7 y^{4} (4 y)}$

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

$\frac{- 12 x^{6} y^{2 + 1} \cdot 21}{7 y^{4} (4 y)}$

Add $2$ and $1$ .

$\frac{- 12 x^{6} y^{3} \cdot 21}{7 y^{4} (4 y)}$

Multiply $y^{4}$ by $y$ by adding the exponents.

Move $y$ .

$\frac{- 12 x^{6} y^{3} \cdot 21}{7 (y \cdot y^{4}) \cdot 4}$

Multiply $y$ by $y^{4}$ .

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

$\frac{- 12 x^{6} y^{3} \cdot 21}{7 (y^{1} y^{4}) \cdot 4}$

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

$\frac{- 12 x^{6} y^{3} \cdot 21}{7 y^{1 + 4} \cdot 4}$

Add $1$ and $4$ .

$\frac{- 12 x^{6} y^{3} \cdot 21}{7 y^{5} \cdot 4}$

Cancel the common factor of $- 12$ and $4$ .

Factor $4$ out of $- 12 x^{6} y^{3} \cdot 21$ .

$\frac{4 (- 3 x^{6} y^{3} \cdot 21)}{7 y^{5} \cdot 4}$

Cancel the common factors.

Factor $4$ out of $7 y^{5} \cdot 4$ .

$\frac{4 (- 3 x^{6} y^{3} \cdot 21)}{4 \cdot (7 y^{5})}$

Cancel the common factor.

$\frac{4 (- 3 x^{6} y^{3} \cdot 21)}{4 \cdot (7 y^{5})}$

Rewrite the expression.

$\frac{- 3 x^{6} y^{3} \cdot 21}{7 y^{5}}$

Cancel the common factor of $y^{3}$ and $y^{5}$ .

Factor $y^{3}$ out of $- 3 x^{6} y^{3} \cdot 21$ .

$\frac{y^{3} (- 3 x^{6} \cdot 21)}{7 y^{5}}$

Cancel the common factors.

Factor $y^{3}$ out of $7 y^{5}$ .

$\frac{y^{3} (- 3 x^{6} \cdot 21)}{y^{3} (7 y^{2})}$

Cancel the common factor.

$\frac{y^{3} (- 3 x^{6} \cdot 21)}{y^{3} (7 y^{2})}$

Rewrite the expression.

$\frac{- 3 x^{6} \cdot 21}{7 y^{2}}$

Cancel the common factor of $21$ and $7$ .

Factor $7$ out of $- 3 x^{6} \cdot 21$ .

$\frac{7 (- 3 x^{6} \cdot 3)}{7 y^{2}}$

Cancel the common factors.

Factor $7$ out of $7 y^{2}$ .

$\frac{7 (- 3 x^{6} \cdot 3)}{7 (y^{2})}$

Cancel the common factor.

$\frac{7 (- 3 x^{6} \cdot 3)}{7 y^{2}}$

Rewrite the expression.

$\frac{- 3 x^{6} \cdot 3}{y^{2}}$

Simplify the expression.

Multiply $3$ by $- 3$ .

$\frac{- 9 x^{6}}{y^{2}}$

Move the negative in front of the fraction.

$- \frac{9 x^{6}}{y^{2}}$

Simplify (-12xy)/(7y^4)*(21x^5y^2)/(4y)

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