Finite Math Examples

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

Step 1

Simplify the expression.

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Step 1.1

Move ${(x^{2} y)}^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 1.2

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

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

Step 1.3

Apply the product rule to $x y$ .

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

Multiply the exponents in ${(x^{2})}^{4}$ .

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Step 2.2.1

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

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

Step 2.2.2

Multiply $2$ by $4$ .

$\frac{x^{3} y^{3}}{x^{8} y^{4}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $x^{3}$ and $x^{8}$ .

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Step 3.1.1

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

$\frac{x^{3} (y^{3})}{x^{8} y^{4}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $x^{3}$ out of $x^{8} y^{4}$ .

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

Step 3.1.2.2

Cancel the common factor.

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

Step 3.1.2.3

Rewrite the expression.

$\frac{y^{3}}{x^{5} y^{4}}$

Step 3.2

Cancel the common factor of $y^{3}$ and $y^{4}$ .

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Step 3.2.1

Multiply by $1$ .

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

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $y^{3}$ out of $x^{5} y^{4}$ .

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

Step 3.2.2.2

Cancel the common factor.

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

Step 3.2.2.3

Rewrite the expression.

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