Algebra Examples

$\frac{32 a b^{4}}{- 8 a^{- 2} b} - 3 a^{3} b^{3}$

Step 1

Simplify each term.

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Step 1.1

Move $a^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{32 a b^{4} a^{2}}{- 8 b} - 3 a^{3} b^{3}$

Step 1.2

Multiply $a$ by $a^{2}$ by adding the exponents.

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Step 1.2.1

Move $a^{2}$ .

$\frac{32 (a^{2} a) b^{4}}{- 8 b} - 3 a^{3} b^{3}$

Step 1.2.2

Multiply $a^{2}$ by $a$ .

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Step 1.2.2.1

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

$\frac{32 (a^{2} a^{1}) b^{4}}{- 8 b} - 3 a^{3} b^{3}$

Step 1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{32 a^{2 + 1} b^{4}}{- 8 b} - 3 a^{3} b^{3}$

Step 1.2.3

Add $2$ and $1$ .

$\frac{32 a^{3} b^{4}}{- 8 b} - 3 a^{3} b^{3}$

Step 1.3

Cancel the common factor of $32$ and $- 8$ .

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Step 1.3.1

Factor $8$ out of $32 a^{3} b^{4}$ .

$\frac{8 (4 a^{3} b^{4})}{- 8 b} - 3 a^{3} b^{3}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $8$ out of $- 8 b$ .

$\frac{8 (4 a^{3} b^{4})}{8 (- b)} - 3 a^{3} b^{3}$

Step 1.3.2.2

Cancel the common factor.

$\frac{8 (4 a^{3} b^{4})}{8 (- b)} - 3 a^{3} b^{3}$

Step 1.3.2.3

Rewrite the expression.

$\frac{4 a^{3} b^{4}}{- b} - 3 a^{3} b^{3}$

Step 1.4

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

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Step 1.4.1

Factor $b$ out of $4 a^{3} b^{4}$ .

$\frac{b (4 a^{3} b^{3})}{- b} - 3 a^{3} b^{3}$

Step 1.4.2

Move the negative one from the denominator of $\frac{4 a^{3} b^{3}}{- 1}$ .

$- 1 \cdot (4 a^{3} b^{3}) - 3 a^{3} b^{3}$

Step 1.5

Rewrite $- 1 \cdot (4 a^{3} b^{3})$ as $- (4 a^{3} b^{3})$ .

$- (4 a^{3} b^{3}) - 3 a^{3} b^{3}$

Step 1.6

Multiply $4$ by $- 1$ .

$- 4 a^{3} b^{3} - 3 a^{3} b^{3}$

Step 2

Subtract $3 a^{3} b^{3}$ from $- 4 a^{3} b^{3}$ .

$- 7 a^{3} b^{3}$