Algebra Examples

$\frac{6 y^{3}}{18 x} \cdot 2 x y$

Step 1

Rewrite using the commutative property of multiplication.

$2 \frac{6 y^{3}}{18 x} (x y)$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $18 x$ .

$2 \frac{6 y^{3}}{2 (9 x)} (x y)$

Step 2.2

Cancel the common factor.

$2 \frac{6 y^{3}}{2 (9 x)} (x y)$

Step 2.3

Rewrite the expression.

$\frac{6 y^{3}}{9 x} (x y)$

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Factor $x$ out of $9 x$ .

$\frac{6 y^{3}}{x \cdot 9} (x y)$

Step 3.2

Factor $x$ out of $x y$ .

$\frac{6 y^{3}}{x \cdot 9} (x (y))$

Step 3.3

Cancel the common factor.

$\frac{6 y^{3}}{x \cdot 9} (x y)$

Step 3.4

Rewrite the expression.

$\frac{6 y^{3}}{9} y$

Step 4

Combine $\frac{6 y^{3}}{9}$ and $y$ .

$\frac{6 y^{3} y}{9}$

Step 5

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

$\frac{6 (y^{1} y^{3})}{9}$

Step 6

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

$\frac{6 y^{1 + 3}}{9}$

Step 7

Add $1$ and $3$ .

$\frac{6 y^{4}}{9}$

Step 8

Cancel the common factor of $6$ and $9$ .

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Step 8.1

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

$\frac{3 (2 y^{4})}{9}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $3$ out of $9$ .

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

$\frac{2 y^{4}}{3}$