Basic Math Examples

$\frac{2 y x^{3}}{x^{- 1} y \cdot 4 x^{4 y}}$

Step 1

Multiply $x^{- 1}$ by $x^{4 y}$ by adding the exponents.

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Step 1.1

Move $x^{4 y}$ .

$\frac{2 y x^{3}}{x^{4 y} x^{- 1} y \cdot 4}$

Step 1.2

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

$\frac{2 y x^{3}}{x^{4 y - 1} y \cdot 4}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $2$ and $4$ .

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Step 2.1.1

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

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

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $x^{4 y - 1} y \cdot 4$ .

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

Step 2.1.2.2

Cancel the common factor.

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

Step 2.1.2.3

Rewrite the expression.

$\frac{y x^{3}}{x^{4 y - 1} y \cdot 2}$

Step 2.2

Cancel the common factor of $y$ .

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Step 2.2.1

Cancel the common factor.

$\frac{y x^{3}}{x^{4 y - 1} y \cdot 2}$

Step 2.2.2

Rewrite the expression.

$\frac{x^{3}}{x^{4 y - 1} \cdot 2}$

Step 2.3

Cancel the common factor of $x^{3}$ and $x^{4 y - 1}$ .

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Step 2.3.1

Factor $x^{4 y - 1}$ out of $x^{3}$ .

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

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $x^{4 y - 1}$ out of $x^{4 y - 1} \cdot 2$ .

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

Step 2.3.2.2

Cancel the common factor.

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

Step 2.3.2.3

Rewrite the expression.

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

Step 3

Simplify the numerator.

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

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

Step 3.1.2

Multiply $4$ by $- 1$ .

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

Step 3.1.3

Multiply $- 1$ by $- 1$ .

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

Step 3.2

Add $3$ and $1$ .

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