Simplify (12xy^4)/(6x^3y^3)*(4x^3y)/(3x^2y^2)

$\frac{12 x y^{4}}{6 x^{3} y^{3}} \cdot \frac{4 x^{3} y}{3 x^{2} y^{2}}$

Step 1

Combine.

$\frac{12 x y^{4} (4 x^{3} y)}{6 x^{3} y^{3} (3 x^{2} y^{2})}$

Step 2

Multiply $x$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$\frac{12 (x^{3} x) y^{4} (4 y)}{6 x^{3} y^{3} (3 x^{2} y^{2})}$

Multiply $x^{3}$ by $x$ .

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

$\frac{12 (x^{3} x^{1}) y^{4} (4 y)}{6 x^{3} y^{3} (3 x^{2} y^{2})}$

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

$\frac{12 x^{3 + 1} y^{4} (4 y)}{6 x^{3} y^{3} (3 x^{2} y^{2})}$

Add $3$ and $1$ .

$\frac{12 x^{4} y^{4} (4 y)}{6 x^{3} y^{3} (3 x^{2} y^{2})}$

Step 3

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

Move $y$ .

$\frac{12 x^{4} (y \cdot y^{4}) \cdot 4}{6 x^{3} y^{3} (3 x^{2} y^{2})}$

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

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

$\frac{12 x^{4} (y^{1} y^{4}) \cdot 4}{6 x^{3} y^{3} (3 x^{2} y^{2})}$

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

$\frac{12 x^{4} y^{1 + 4} \cdot 4}{6 x^{3} y^{3} (3 x^{2} y^{2})}$

Add $1$ and $4$ .

$\frac{12 x^{4} y^{5} \cdot 4}{6 x^{3} y^{3} (3 x^{2} y^{2})}$

Step 4

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

Move $x^{2}$ .

$\frac{12 x^{4} y^{5} \cdot 4}{6 (x^{2} x^{3}) y^{3} (3 y^{2})}$

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

$\frac{12 x^{4} y^{5} \cdot 4}{6 x^{2 + 3} y^{3} (3 y^{2})}$

Add $2$ and $3$ .

$\frac{12 x^{4} y^{5} \cdot 4}{6 x^{5} y^{3} (3 y^{2})}$

Step 5

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

Move $y^{2}$ .

$\frac{12 x^{4} y^{5} \cdot 4}{6 x^{5} (y^{2} y^{3}) \cdot 3}$

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

$\frac{12 x^{4} y^{5} \cdot 4}{6 x^{5} y^{2 + 3} \cdot 3}$

Add $2$ and $3$ .

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

Step 6

Cancel the common factor of $12$ and $6$ .

Factor $6$ out of $12 x^{4} y^{5} \cdot 4$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 x^{4} y^{5} \cdot 4}{x^{5} y^{5} \cdot 3}$

Step 7

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

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

$\frac{x^{4} (2 y^{5} \cdot 4)}{x^{5} y^{5} \cdot 3}$

Cancel the common factors.

Factor $x^{4}$ out of $x^{5} y^{5} \cdot 3$ .

$\frac{x^{4} (2 y^{5} \cdot 4)}{x^{4} (x y^{5} \cdot 3)}$

Cancel the common factor.

$\frac{x^{4} (2 y^{5} \cdot 4)}{x^{4} (x y^{5} \cdot 3)}$

Rewrite the expression.

$\frac{2 y^{5} \cdot 4}{x y^{5} \cdot 3}$

Step 8

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

Cancel the common factor.

$\frac{2 y^{5} \cdot 4}{x y^{5} \cdot 3}$

Rewrite the expression.

$\frac{2 \cdot 4}{x \cdot 3}$

Step 9

Simplify the expression.

Multiply $2$ by $4$ .

$\frac{8}{x \cdot 3}$

Move $3$ to the left of $x$ .

$\frac{8}{3 x}$

Simplify (12xy^4)/(6x^3y^3)*(4x^3y)/(3x^2y^2)

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