Finite Math Examples

$\frac{{(- x^{0} y^{4})}^{- 5}}{y x^{2} \cdot (- x^{2} y^{- 4})}$

Step 1

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

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Step 1.1

Move $y^{- 4}$ .

$\frac{{(- x^{0} y^{4})}^{- 5}}{y^{- 4} y x^{2} \cdot (- x^{2})}$

Step 1.2

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

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Step 1.2.1

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

$\frac{{(- x^{0} y^{4})}^{- 5}}{y^{- 4} y^{1} x^{2} \cdot (- x^{2})}$

Step 1.2.2

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

$\frac{{(- x^{0} y^{4})}^{- 5}}{y^{- 4 + 1} x^{2} \cdot (- x^{2})}$

Step 1.3

Add $- 4$ and $1$ .

$\frac{{(- x^{0} y^{4})}^{- 5}}{y^{- 3} x^{2} \cdot (- x^{2})}$

Step 2

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 2.1

Move $x^{2}$ .

$\frac{{(- x^{0} y^{4})}^{- 5}}{y^{- 3} (x^{2} x^{2}) \cdot - 1}$

Step 2.2

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

$\frac{{(- x^{0} y^{4})}^{- 5}}{y^{- 3} x^{2 + 2} \cdot - 1}$

Step 2.3

Add $2$ and $2$ .

$\frac{{(- x^{0} y^{4})}^{- 5}}{y^{- 3} x^{4} \cdot - 1}$

Step 3

Simplify the expression.

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Step 3.1

Move ${(- x^{0} y^{4})}^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{y^{- 3} x^{4} \cdot - 1 {(- x^{0} y^{4})}^{5}}$

Step 3.2

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

$\frac{y^{3}}{x^{4} \cdot - 1 {(- 1 y^{4})}^{5}}$

Step 4

Simplify the denominator.

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Step 4.1

Factor out negative.

$\frac{y^{3}}{- x^{4} {(- 1 y^{4})}^{5}}$

Step 4.2

Rewrite $- 1 y^{4}$ as $- y^{4}$ .

$\frac{y^{3}}{- x^{4} {(- y^{4})}^{5}}$

Step 4.3

Apply the product rule to $- y^{4}$ .

$\frac{y^{3}}{- x^{4} ({(- 1)}^{5} {(y^{4})}^{5})}$

Step 4.4

Raise $- 1$ to the power of $5$ .

$\frac{y^{3}}{- x^{4} (- {(y^{4})}^{5})}$

Step 4.5

Multiply the exponents in ${(y^{4})}^{5}$ .

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Step 4.5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{y^{3}}{- x^{4} (- y^{4 \cdot 5})}$

Step 4.5.2

Multiply $4$ by $5$ .

$\frac{y^{3}}{- x^{4} (- y^{20})}$

$\frac{y^{3}}{- x^{4} \cdot - 1 y^{20}}$

Step 4.6

Combine exponents.

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Step 4.6.1

Factor out negative.

$\frac{y^{3}}{- (x^{4} \cdot - 1 y^{20})}$

Step 4.6.2

Multiply $- 1$ by $- 1$ .

$\frac{y^{3}}{1 (x^{4} y^{20})}$

Step 4.6.3

Multiply $x^{4}$ by $1$ .

$\frac{y^{3}}{x^{4} y^{20}}$

Step 5

Cancel the common factor of $y^{3}$ and $y^{20}$ .

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Step 5.1

Multiply by $1$ .

$\frac{y^{3} \cdot 1}{x^{4} y^{20}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $y^{3}$ out of $x^{4} y^{20}$ .

$\frac{y^{3} \cdot 1}{y^{3} (x^{4} y^{17})}$

Step 5.2.2

Cancel the common factor.

$\frac{y^{3} \cdot 1}{y^{3} (x^{4} y^{17})}$

Step 5.2.3

Rewrite the expression.

$\frac{1}{x^{4} y^{17}}$