Algebra Examples

$\frac{{(- 6 x^{4} y^{6})}^{2}}{{(- 3 x^{3} y^{5})}^{2}} - 7 x^{2} y^{2}$

Step 1

Simplify each term.

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Step 1.1

Simplify the numerator.

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Step 1.1.1

Apply the product rule to $- 6 x^{4} y^{6}$ .

$\frac{{(- 6 x^{4})}^{2} {(y^{6})}^{2}}{{(- 3 x^{3} y^{5})}^{2}} - 7 x^{2} y^{2}$

Step 1.1.2

Apply the product rule to $- 6 x^{4}$ .

$\frac{{(- 6)}^{2} {(x^{4})}^{2} {(y^{6})}^{2}}{{(- 3 x^{3} y^{5})}^{2}} - 7 x^{2} y^{2}$

Step 1.1.3

Raise $- 6$ to the power of $2$ .

$\frac{36 {(x^{4})}^{2} {(y^{6})}^{2}}{{(- 3 x^{3} y^{5})}^{2}} - 7 x^{2} y^{2}$

Step 1.1.4

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

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Step 1.1.4.1

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

$\frac{36 x^{4 \cdot 2} {(y^{6})}^{2}}{{(- 3 x^{3} y^{5})}^{2}} - 7 x^{2} y^{2}$

Step 1.1.4.2

Multiply $4$ by $2$ .

$\frac{36 x^{8} {(y^{6})}^{2}}{{(- 3 x^{3} y^{5})}^{2}} - 7 x^{2} y^{2}$

Step 1.1.5

Multiply the exponents in ${(y^{6})}^{2}$ .

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Step 1.1.5.1

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

$\frac{36 x^{8} y^{6 \cdot 2}}{{(- 3 x^{3} y^{5})}^{2}} - 7 x^{2} y^{2}$

Step 1.1.5.2

Multiply $6$ by $2$ .

$\frac{36 x^{8} y^{12}}{{(- 3 x^{3} y^{5})}^{2}} - 7 x^{2} y^{2}$

Step 1.2

Simplify the denominator.

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Step 1.2.1

Apply the product rule to $- 3 x^{3} y^{5}$ .

$\frac{36 x^{8} y^{12}}{{(- 3 x^{3})}^{2} {(y^{5})}^{2}} - 7 x^{2} y^{2}$

Step 1.2.2

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

$\frac{36 x^{8} y^{12}}{{(- 3)}^{2} {(x^{3})}^{2} {(y^{5})}^{2}} - 7 x^{2} y^{2}$

Step 1.2.3

Raise $- 3$ to the power of $2$ .

$\frac{36 x^{8} y^{12}}{9 {(x^{3})}^{2} {(y^{5})}^{2}} - 7 x^{2} y^{2}$

Step 1.2.4

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

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Step 1.2.4.1

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

$\frac{36 x^{8} y^{12}}{9 x^{3 \cdot 2} {(y^{5})}^{2}} - 7 x^{2} y^{2}$

Step 1.2.4.2

Multiply $3$ by $2$ .

$\frac{36 x^{8} y^{12}}{9 x^{6} {(y^{5})}^{2}} - 7 x^{2} y^{2}$

Step 1.2.5

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

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Step 1.2.5.1

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

$\frac{36 x^{8} y^{12}}{9 x^{6} y^{5 \cdot 2}} - 7 x^{2} y^{2}$

Step 1.2.5.2

Multiply $5$ by $2$ .

$\frac{36 x^{8} y^{12}}{9 x^{6} y^{10}} - 7 x^{2} y^{2}$

Step 1.3

Cancel the common factor of $36$ and $9$ .

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Step 1.3.1

Factor $9$ out of $36 x^{8} y^{12}$ .

$\frac{9 (4 x^{8} y^{12})}{9 x^{6} y^{10}} - 7 x^{2} y^{2}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $9$ out of $9 x^{6} y^{10}$ .

$\frac{9 (4 x^{8} y^{12})}{9 (x^{6} y^{10})} - 7 x^{2} y^{2}$

Step 1.3.2.2

Cancel the common factor.

$\frac{9 (4 x^{8} y^{12})}{9 (x^{6} y^{10})} - 7 x^{2} y^{2}$

Step 1.3.2.3

Rewrite the expression.

$\frac{4 x^{8} y^{12}}{x^{6} y^{10}} - 7 x^{2} y^{2}$

Step 1.4

Cancel the common factor of $x^{8}$ and $x^{6}$ .

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Step 1.4.1

Factor $x^{6}$ out of $4 x^{8} y^{12}$ .

$\frac{x^{6} (4 x^{2} y^{12})}{x^{6} y^{10}} - 7 x^{2} y^{2}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $x^{6}$ out of $x^{6} y^{10}$ .

$\frac{x^{6} (4 x^{2} y^{12})}{x^{6} (y^{10})} - 7 x^{2} y^{2}$

Step 1.4.2.2

Cancel the common factor.

$\frac{x^{6} (4 x^{2} y^{12})}{x^{6} y^{10}} - 7 x^{2} y^{2}$

Step 1.4.2.3

Rewrite the expression.

$\frac{4 x^{2} y^{12}}{y^{10}} - 7 x^{2} y^{2}$

Step 1.5

Cancel the common factor of $y^{12}$ and $y^{10}$ .

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Step 1.5.1

Factor $y^{10}$ out of $4 x^{2} y^{12}$ .

$\frac{y^{10} (4 x^{2} y^{2})}{y^{10}} - 7 x^{2} y^{2}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Multiply by $1$ .

$\frac{y^{10} (4 x^{2} y^{2})}{y^{10} \cdot 1} - 7 x^{2} y^{2}$

Step 1.5.2.2

Cancel the common factor.

$\frac{y^{10} (4 x^{2} y^{2})}{y^{10} \cdot 1} - 7 x^{2} y^{2}$

Step 1.5.2.3

Rewrite the expression.

$\frac{4 x^{2} y^{2}}{1} - 7 x^{2} y^{2}$

Step 1.5.2.4

Divide $4 x^{2} y^{2}$ by $1$ .

$4 x^{2} y^{2} - 7 x^{2} y^{2}$

Step 2

Subtract $7 x^{2} y^{2}$ from $4 x^{2} y^{2}$ .

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