Trigonometry Examples

$\frac{- 3 x y}{9 x^{3} y^{- 4}}$

Step 1

Move $y^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 3 x y \cdot y^{4}}{9 x^{3}}$

Step 2

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

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Step 2.1

Move $y^{4}$ .

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

Step 2.2

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

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Step 2.2.1

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

$\frac{- 3 x (y^{4} y^{1})}{9 x^{3}}$

Step 2.2.2

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

$\frac{- 3 x y^{4 + 1}}{9 x^{3}}$

Step 2.3

Add $4$ and $1$ .

$\frac{- 3 x y^{5}}{9 x^{3}}$

Step 3

Cancel the common factor of $- 3$ and $9$ .

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Step 3.1

Factor $3$ out of $- 3 x y^{5}$ .

$\frac{3 (- x y^{5})}{9 x^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $9 x^{3}$ .

$\frac{3 (- x y^{5})}{3 (3 x^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (- x y^{5})}{3 (3 x^{3})}$

Step 3.2.3

Rewrite the expression.

$\frac{- x y^{5}}{3 x^{3}}$

Step 4

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

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Step 4.1

Factor $x$ out of $- x y^{5}$ .

$\frac{x (- 1 y^{5})}{3 x^{3}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\frac{x (- 1 y^{5})}{x (3 x^{2})}$

Step 4.2.2

Cancel the common factor.

$\frac{x (- 1 y^{5})}{x (3 x^{2})}$

Step 4.2.3

Rewrite the expression.

$\frac{- 1 y^{5}}{3 x^{2}}$

Step 5

Move the negative in front of the fraction.

$- \frac{y^{5}}{3 x^{2}}$