Simplify (12x^7y^11)/(2x^4y^5)*(-5x^6y^10)/(3y)

$\frac{12 x^{7} y^{11}}{2 x^{4} y^{5}} \cdot \frac{- 5 x^{6} y^{10}}{3 y}$

Step 1

Combine.

$\frac{12 x^{7} y^{11} (- 5 x^{6} y^{10})}{2 x^{4} y^{5} (3 y)}$

Step 2

Multiply $x^{7}$ by $x^{6}$ by adding the exponents.

Move $x^{6}$ .

$\frac{12 (x^{6} x^{7}) y^{11} (- 5 y^{10})}{2 x^{4} y^{5} (3 y)}$

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

$\frac{12 x^{6 + 7} y^{11} (- 5 y^{10})}{2 x^{4} y^{5} (3 y)}$

Add $6$ and $7$ .

$\frac{12 x^{13} y^{11} (- 5 y^{10})}{2 x^{4} y^{5} (3 y)}$

Step 3

Multiply $y^{11}$ by $y^{10}$ by adding the exponents.

Move $y^{10}$ .

$\frac{12 x^{13} (y^{10} y^{11}) \cdot - 5}{2 x^{4} y^{5} (3 y)}$

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

$\frac{12 x^{13} y^{10 + 11} \cdot - 5}{2 x^{4} y^{5} (3 y)}$

Add $10$ and $11$ .

$\frac{12 x^{13} y^{21} \cdot - 5}{2 x^{4} y^{5} (3 y)}$

Step 4

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

Move $y$ .

$\frac{12 x^{13} y^{21} \cdot - 5}{2 x^{4} (y \cdot y^{5}) \cdot 3}$

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

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

$\frac{12 x^{13} y^{21} \cdot - 5}{2 x^{4} (y^{1} y^{5}) \cdot 3}$

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

$\frac{12 x^{13} y^{21} \cdot - 5}{2 x^{4} y^{1 + 5} \cdot 3}$

Add $1$ and $5$ .

$\frac{12 x^{13} y^{21} \cdot - 5}{2 x^{4} y^{6} \cdot 3}$

Step 5

Cancel the common factor of $12$ and $2$ .

Factor $2$ out of $12 x^{13} y^{21} \cdot - 5$ .

$\frac{2 (6 x^{13} y^{21} \cdot - 5)}{2 x^{4} y^{6} \cdot 3}$

Cancel the common factors.

Factor $2$ out of $2 x^{4} y^{6} \cdot 3$ .

$\frac{2 (6 x^{13} y^{21} \cdot - 5)}{2 (x^{4} y^{6} \cdot 3)}$

Cancel the common factor.

$\frac{2 (6 x^{13} y^{21} \cdot - 5)}{2 (x^{4} y^{6} \cdot 3)}$

Rewrite the expression.

$\frac{6 x^{13} y^{21} \cdot - 5}{x^{4} y^{6} \cdot 3}$

Step 6

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 x^{13} y^{21} \cdot - 5$ .

$\frac{3 (2 x^{13} y^{21} \cdot - 5)}{x^{4} y^{6} \cdot 3}$

Cancel the common factors.

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

$\frac{3 (2 x^{13} y^{21} \cdot - 5)}{3 \cdot (x^{4} y^{6})}$

Cancel the common factor.

$\frac{3 (2 x^{13} y^{21} \cdot - 5)}{3 \cdot (x^{4} y^{6})}$

Rewrite the expression.

$\frac{2 x^{13} y^{21} \cdot - 5}{x^{4} y^{6}}$

Step 7

Cancel the common factor of $x^{13}$ and $x^{4}$ .

Factor $x^{4}$ out of $2 x^{13} y^{21} \cdot - 5$ .

$\frac{x^{4} (2 x^{9} y^{21} \cdot - 5)}{x^{4} y^{6}}$

Cancel the common factors.

Factor $x^{4}$ out of $x^{4} y^{6}$ .

$\frac{x^{4} (2 x^{9} y^{21} \cdot - 5)}{x^{4} (y^{6})}$

Cancel the common factor.

$\frac{x^{4} (2 x^{9} y^{21} \cdot - 5)}{x^{4} y^{6}}$

Rewrite the expression.

$\frac{2 x^{9} y^{21} \cdot - 5}{y^{6}}$

Step 8

Cancel the common factor of $y^{21}$ and $y^{6}$ .

Factor $y^{6}$ out of $2 x^{9} y^{21} \cdot - 5$ .

$\frac{y^{6} (2 x^{9} y^{15} \cdot - 5)}{y^{6}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{y^{6} (2 x^{9} y^{15} \cdot - 5)}{y^{6} \cdot 1}$

Cancel the common factor.

$\frac{y^{6} (2 x^{9} y^{15} \cdot - 5)}{y^{6} \cdot 1}$

Rewrite the expression.

$\frac{2 x^{9} y^{15} \cdot - 5}{1}$

Divide $2 x^{9} y^{15} \cdot - 5$ by $1$ .

$2 x^{9} y^{15} \cdot - 5$

Step 9

Multiply $- 5$ by $2$ .

$- 10 x^{9} y^{15}$

Simplify (12x^7y^11)/(2x^4y^5)*(-5x^6y^10)/(3y)

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