Finite Math Examples

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

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Simplify the numerator.

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Step 1.1.1

Apply the product rule to $x^{2} y^{- 3}$ .

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

Step 1.1.2

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 1.1.2.1

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

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

Step 1.1.2.2

Multiply $2$ by $2$ .

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

Step 1.1.3

Multiply the exponents in ${(y^{- 3})}^{2}$ .

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Step 1.1.3.1

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

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

Step 1.1.3.2

Multiply $- 3$ by $2$ .

$\frac{x^{4} y^{- 6}}{x^{4} y^{5}}$

Step 1.1.4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x^{4} \frac{1}{y^{6}}}{x^{4} y^{5}}$

Step 1.2

Combine $x^{4}$ and $\frac{1}{y^{6}}$ .

$\frac{\frac{x^{4}}{y^{6}}}{x^{4} y^{5}}$

Step 1.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{x^{4}}{y^{6}} \cdot \frac{1}{x^{4} y^{5}}$

Step 1.4

Combine.

$\frac{x^{4} \cdot 1}{y^{6} (x^{4} y^{5})}$

Step 1.5

Multiply $y^{6}$ by $y^{5}$ by adding the exponents.

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Step 1.5.1

Move $y^{5}$ .

$\frac{x^{4} \cdot 1}{y^{5} y^{6} x^{4}}$

Step 1.5.2

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

$\frac{x^{4} \cdot 1}{y^{5 + 6} x^{4}}$

Step 1.5.3

Add $5$ and $6$ .

$\frac{x^{4} \cdot 1}{y^{11} x^{4}}$

Step 1.6

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

$\frac{x^{4}}{y^{11} x^{4}}$

Step 1.7

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

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Step 1.7.1

Cancel the common factor.

$\frac{x^{4}}{y^{11} x^{4}}$

Step 1.7.2

Rewrite the expression.

$\frac{1}{y^{11}}$

Step 2

The degree cannot be determined because $\frac{1}{y^{11}}$ is not a polynomial.

Not a polynomial