Algebra Examples

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

Step 1

Move $x^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

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

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Step 2.1

Move $x^{3}$ .

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.3

Add $3$ and $1$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Factor $y$ out of $y^{1}$ .

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

Step 3.2.3

Cancel the common factor.

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

Step 3.2.4

Rewrite the expression.

$\frac{y x^{4}}{1}$

Step 3.2.5

Divide $y x^{4}$ by $1$ .

$y x^{4}$