Finite Math Examples

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

Step 1

Simplify the expression.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Move ${(x^{2} y^{- 3})}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

Multiply $2$ by $3$ .

$\frac{x^{6} {(y^{- 3})}^{3}}{x^{3} y^{4}}$

Step 2.3

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

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Step 2.3.1

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

$\frac{x^{6} y^{- 3 \cdot 3}}{x^{3} y^{4}}$

Step 2.3.2

Multiply $- 3$ by $3$ .

$\frac{x^{6} y^{- 9}}{x^{3} y^{4}}$

Step 2.4

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

$\frac{x^{6} \frac{1}{y^{9}}}{x^{3} y^{4}}$

Step 3

Combine $x^{6}$ and $\frac{1}{y^{9}}$ .

$\frac{\frac{x^{6}}{y^{9}}}{x^{3} y^{4}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{x^{6}}{y^{9}} \cdot \frac{1}{x^{3} y^{4}}$

Step 5

Combine.

$\frac{x^{6} \cdot 1}{y^{9} (x^{3} y^{4})}$

Step 6

Multiply $y^{9}$ by $y^{4}$ by adding the exponents.

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Step 6.1

Move $y^{4}$ .

$\frac{x^{6} \cdot 1}{y^{4} y^{9} x^{3}}$

Step 6.2

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

$\frac{x^{6} \cdot 1}{y^{4 + 9} x^{3}}$

Step 6.3

Add $4$ and $9$ .

$\frac{x^{6} \cdot 1}{y^{13} x^{3}}$

Step 7

Multiply $x^{6}$ by $1$ .

$\frac{x^{6}}{y^{13} x^{3}}$

Step 8

Cancel the common factor of $x^{6}$ and $x^{3}$ .

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Step 8.1

Factor $x^{3}$ out of $x^{6}$ .

$\frac{x^{3} x^{3}}{y^{13} x^{3}}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $x^{3}$ out of $y^{13} x^{3}$ .

$\frac{x^{3} x^{3}}{x^{3} y^{13}}$

Step 8.2.2

Cancel the common factor.

$\frac{x^{3} x^{3}}{x^{3} y^{13}}$

Step 8.2.3

Rewrite the expression.

$\frac{x^{3}}{y^{13}}$