Finite Math Examples

$\frac{- 2 x^{2} y^{5}}{{(6 x^{3} y)}^{3}}$

Step 1

Simplify the denominator.

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Step 1.1

Apply the product rule to $6 x^{3} y$ .

$\frac{- 2 x^{2} y^{5}}{{(6 x^{3})}^{3} y^{3}}$

Step 1.2

Apply the product rule to $6 x^{3}$ .

$\frac{- 2 x^{2} y^{5}}{6^{3} {(x^{3})}^{3} y^{3}}$

Step 1.3

Raise $6$ to the power of $3$ .

$\frac{- 2 x^{2} y^{5}}{216 {(x^{3})}^{3} y^{3}}$

Step 1.4

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

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Step 1.4.1

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

$\frac{- 2 x^{2} y^{5}}{216 x^{3 \cdot 3} y^{3}}$

Step 1.4.2

Multiply $3$ by $3$ .

$\frac{- 2 x^{2} y^{5}}{216 x^{9} y^{3}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $- 2$ and $216$ .

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Step 2.1.1

Factor $2$ out of $- 2 x^{2} y^{5}$ .

$\frac{2 (- x^{2} y^{5})}{216 x^{9} y^{3}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $216 x^{9} y^{3}$ .

$\frac{2 (- x^{2} y^{5})}{2 (108 x^{9} y^{3})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{2 (- x^{2} y^{5})}{2 (108 x^{9} y^{3})}$

Step 2.1.2.3

Rewrite the expression.

$\frac{- x^{2} y^{5}}{108 x^{9} y^{3}}$

Step 2.2

Cancel the common factor of $x^{2}$ and $x^{9}$ .

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Step 2.2.1

Factor $x^{2}$ out of $- x^{2} y^{5}$ .

$\frac{x^{2} (- 1 y^{5})}{108 x^{9} y^{3}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $x^{2}$ out of $108 x^{9} y^{3}$ .

$\frac{x^{2} (- 1 y^{5})}{x^{2} (108 x^{7} y^{3})}$

Step 2.2.2.2

Cancel the common factor.

$\frac{x^{2} (- 1 y^{5})}{x^{2} (108 x^{7} y^{3})}$

Step 2.2.2.3

Rewrite the expression.

$\frac{- 1 y^{5}}{108 x^{7} y^{3}}$

Step 2.3

Cancel the common factor of $y^{5}$ and $y^{3}$ .

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Step 2.3.1

Factor $y^{3}$ out of $- 1 y^{5}$ .

$\frac{y^{3} (- 1 y^{2})}{108 x^{7} y^{3}}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $y^{3}$ out of $108 x^{7} y^{3}$ .

$\frac{y^{3} (- 1 y^{2})}{y^{3} (108 x^{7})}$

Step 2.3.2.2

Cancel the common factor.

$\frac{y^{3} (- 1 y^{2})}{y^{3} (108 x^{7})}$

Step 2.3.2.3

Rewrite the expression.

$\frac{- 1 y^{2}}{108 x^{7}}$

Step 2.4

Move the negative in front of the fraction.

$- \frac{y^{2}}{108 x^{7}}$