Simplify (x^2y)/(4xy)x/6(3y^5)/(x^4)

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

Step 1

Combine.

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

Step 2

Combine.

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

Step 3

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

Move $x$ .

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

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

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

$\frac{x^{1} x^{2} y (3 y^{5})}{4 x y \cdot 6 x^{4}}$

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

$\frac{x^{1 + 2} y (3 y^{5})}{4 x y \cdot 6 x^{4}}$

Add $1$ and $2$ .

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

Step 4

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

Move $y^{5}$ .

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

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

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

$\frac{x^{3} (y^{5} y^{1}) \cdot 3}{4 x y \cdot 6 x^{4}}$

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

$\frac{x^{3} y^{5 + 1} \cdot 3}{4 x y \cdot 6 x^{4}}$

Add $5$ and $1$ .

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

Step 5

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

Move $x^{4}$ .

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

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

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

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

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

$\frac{x^{3} y^{6} \cdot 3}{4 x^{4 + 1} y \cdot 6}$

Add $4$ and $1$ .

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

Step 6

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

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

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

Cancel the common factors.

Factor $x^{3}$ out of $4 x^{5} y \cdot 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 7

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 8

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 9

Multiply $2$ by $4$ .

$\frac{y^{5}}{8 x^{2}}$

Simplify (x^2y)/(4xy)*x/6*(3y^5)/(x^4)

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Simplify (x^2y)/(4xy)x/6(3y^5)/(x^4)