Algebra Examples

$\frac{{(- 6 a^{5} b)}^{2}}{12 a^{7} b} - 8 a^{3} b$

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 $- 6 a^{5} b$ .

$\frac{{(- 6 a^{5})}^{2} b^{2}}{12 a^{7} b} - 8 a^{3} b$

Step 1.1.2

Apply the product rule to $- 6 a^{5}$ .

$\frac{{(- 6)}^{2} {(a^{5})}^{2} b^{2}}{12 a^{7} b} - 8 a^{3} b$

Step 1.1.3

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

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

Step 1.1.4

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

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Step 1.1.4.1

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

$\frac{36 a^{5 \cdot 2} b^{2}}{12 a^{7} b} - 8 a^{3} b$

Step 1.1.4.2

Multiply $5$ by $2$ .

$\frac{36 a^{10} b^{2}}{12 a^{7} b} - 8 a^{3} b$

Step 1.2

Cancel the common factor of $36$ and $12$ .

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Step 1.2.1

Factor $12$ out of $36 a^{10} b^{2}$ .

$\frac{12 (3 a^{10} b^{2})}{12 a^{7} b} - 8 a^{3} b$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $12$ out of $12 a^{7} b$ .

$\frac{12 (3 a^{10} b^{2})}{12 (a^{7} b)} - 8 a^{3} b$

Step 1.2.2.2

Cancel the common factor.

$\frac{12 (3 a^{10} b^{2})}{12 (a^{7} b)} - 8 a^{3} b$

Step 1.2.2.3

Rewrite the expression.

$\frac{3 a^{10} b^{2}}{a^{7} b} - 8 a^{3} b$

Step 1.3

Cancel the common factor of $a^{10}$ and $a^{7}$ .

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Step 1.3.1

Factor $a^{7}$ out of $3 a^{10} b^{2}$ .

$\frac{a^{7} (3 a^{3} b^{2})}{a^{7} b} - 8 a^{3} b$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $a^{7}$ out of $a^{7} b$ .

$\frac{a^{7} (3 a^{3} b^{2})}{a^{7} (b)} - 8 a^{3} b$

Step 1.3.2.2

Cancel the common factor.

$\frac{a^{7} (3 a^{3} b^{2})}{a^{7} b} - 8 a^{3} b$

Step 1.3.2.3

Rewrite the expression.

$\frac{3 a^{3} b^{2}}{b} - 8 a^{3} b$

Step 1.4

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

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Step 1.4.1

Factor $b$ out of $3 a^{3} b^{2}$ .

$\frac{b (3 a^{3} b)}{b} - 8 a^{3} b$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Raise $b$ to the power of $1$ .

$\frac{b (3 a^{3} b)}{b^{1}} - 8 a^{3} b$

Step 1.4.2.2

Factor $b$ out of $b^{1}$ .

$\frac{b (3 a^{3} b)}{b \cdot 1} - 8 a^{3} b$

Step 1.4.2.3

Cancel the common factor.

$\frac{b (3 a^{3} b)}{b \cdot 1} - 8 a^{3} b$

Step 1.4.2.4

Rewrite the expression.

$\frac{3 a^{3} b}{1} - 8 a^{3} b$

Step 1.4.2.5

Divide $3 a^{3} b$ by $1$ .

$3 a^{3} b - 8 a^{3} b$

Step 2

Subtract $8 a^{3} b$ from $3 a^{3} b$ .

$- 5 a^{3} b$