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

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

Step 1

Combine.

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

Step 2

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

Move $y$ .

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

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

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

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

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

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

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

Add $1$ and $2$ .

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

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

Step 3

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

Factor $x$ out of $x^{3} (6 y^{4})$ .

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

Cancel the common factors.

Factor $x$ out of $2 y^{3} x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 4

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $x^{2} (6 y^{4})$ .

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

Cancel the common factors.

Factor $2$ out of $2 y^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 5

Cancel the common factor of $y^{4}$ and $y^{3}$ .

Factor $y^{3}$ out of $x^{2} (3 y^{4})$ .

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $x^{2} (3 y)$ by $1$ .

$x^{2} (3 y)$

$x^{2} (3 y)$

$x^{2} (3 y)$

Step 6

Rewrite using the commutative property of multiplication.

$3 x^{2} y$

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