Algebra Examples

$\frac{- 60 x^{8} y^{13}}{{(2 x^{2} y^{3})}^{5} - 12 x^{10} y^{15}}$

Step 1

Simplify the denominator.

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Step 1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1.1

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

$\frac{- 60 x^{8} y^{13}}{{(2 x^{2})}^{5} {(y^{3})}^{5} - 12 x^{10} y^{15}}$

Step 1.1.2

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

$\frac{- 60 x^{8} y^{13}}{2^{5} {(x^{2})}^{5} {(y^{3})}^{5} - 12 x^{10} y^{15}}$

Step 1.2

Raise $2$ to the power of $5$ .

$\frac{- 60 x^{8} y^{13}}{32 {(x^{2})}^{5} {(y^{3})}^{5} - 12 x^{10} y^{15}}$

Step 1.3

Multiply the exponents in ${(x^{2})}^{5}$ .

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Step 1.3.1

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

$\frac{- 60 x^{8} y^{13}}{32 x^{2 \cdot 5} {(y^{3})}^{5} - 12 x^{10} y^{15}}$

Step 1.3.2

Multiply $2$ by $5$ .

$\frac{- 60 x^{8} y^{13}}{32 x^{10} {(y^{3})}^{5} - 12 x^{10} y^{15}}$

Step 1.4

Multiply the exponents in ${(y^{3})}^{5}$ .

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Step 1.4.1

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

$\frac{- 60 x^{8} y^{13}}{32 x^{10} y^{3 \cdot 5} - 12 x^{10} y^{15}}$

Step 1.4.2

Multiply $3$ by $5$ .

$\frac{- 60 x^{8} y^{13}}{32 x^{10} y^{15} - 12 x^{10} y^{15}}$

Step 1.5

Subtract $12 x^{10} y^{15}$ from $32 x^{10} y^{15}$ .

$\frac{- 60 x^{8} y^{13}}{20 x^{10} y^{15}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $- 60$ and $20$ .

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Step 2.1.1

Factor $20$ out of $- 60 x^{8} y^{13}$ .

$\frac{20 (- 3 x^{8} y^{13})}{20 x^{10} y^{15}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $20$ out of $20 x^{10} y^{15}$ .

$\frac{20 (- 3 x^{8} y^{13})}{20 (x^{10} y^{15})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{20 (- 3 x^{8} y^{13})}{20 (x^{10} y^{15})}$

Step 2.1.2.3

Rewrite the expression.

$\frac{- 3 x^{8} y^{13}}{x^{10} y^{15}}$

Step 2.2

Cancel the common factor of $x^{8}$ and $x^{10}$ .

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Step 2.2.1

Factor $x^{8}$ out of $- 3 x^{8} y^{13}$ .

$\frac{x^{8} (- 3 y^{13})}{x^{10} y^{15}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $x^{8}$ out of $x^{10} y^{15}$ .

$\frac{x^{8} (- 3 y^{13})}{x^{8} (x^{2} y^{15})}$

Step 2.2.2.2

Cancel the common factor.

$\frac{x^{8} (- 3 y^{13})}{x^{8} (x^{2} y^{15})}$

Step 2.2.2.3

Rewrite the expression.

$\frac{- 3 y^{13}}{x^{2} y^{15}}$

Step 2.3

Cancel the common factor of $y^{13}$ and $y^{15}$ .

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Step 2.3.1

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

$\frac{y^{13} \cdot - 3}{x^{2} y^{15}}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $y^{13}$ out of $x^{2} y^{15}$ .

$\frac{y^{13} \cdot - 3}{y^{13} (x^{2} y^{2})}$

Step 2.3.2.2

Cancel the common factor.

$\frac{y^{13} \cdot - 3}{y^{13} (x^{2} y^{2})}$

Step 2.3.2.3

Rewrite the expression.

$\frac{- 3}{x^{2} y^{2}}$

Step 2.4

Move the negative in front of the fraction.

$- \frac{3}{x^{2} y^{2}}$