Pre-Algebra Examples

$\frac{(2 x y) (x^{3})}{8 x^{2 y^{4}}}$

Step 1

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

Tap for more steps...

Step 1.1

Move $x^{3}$ .

$\frac{2 (x^{3} x) y}{8 x^{2 y^{4}}}$

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

$\frac{2 (x^{3} x^{1}) y}{8 x^{2 y^{4}}}$

Step 1.2.2

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

$\frac{2 x^{3 + 1} y}{8 x^{2 y^{4}}}$

Step 1.3

Add $3$ and $1$ .

$\frac{2 x^{4} y}{8 x^{2 y^{4}}}$

Step 2

Cancel the common factor of $2$ and $8$ .

Tap for more steps...

Step 2.1

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

$\frac{2 (x^{4} y)}{8 x^{2 y^{4}}}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $2$ out of $8 x^{2 y^{4}}$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factor of $x^{4}$ and $x^{2 y^{4}}$ .

Tap for more steps...

Step 3.1

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

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

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$\frac{x^{4 - 2 y^{4}} y}{4}$

Step 4

Reorder factors in $\frac{x^{4 - 2 y^{4}} y}{4}$ .

$\frac{y x^{4 - 2 y^{4}}}{4}$