Basic Math Examples

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

Step 1

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

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Step 1.1

Move $a$ .

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

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

$\frac{{(2 a^{3} b^{4})}^{2}}{a^{1 + 2} \cdot (- 1 b)}$

Step 1.3

Add $1$ and $2$ .

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

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $2 a^{3} b^{4}$ .

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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Step 2.4.1

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

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

Step 2.4.2

Multiply $3$ by $2$ .

$\frac{4 a^{6} {(b^{4})}^{2}}{a^{3} \cdot - 1 b}$

Step 2.5

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

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Step 2.5.1

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

$\frac{4 a^{6} b^{4 \cdot 2}}{a^{3} \cdot - 1 b}$

Step 2.5.2

Multiply $4$ by $2$ .

$\frac{4 a^{6} b^{8}}{a^{3} \cdot - 1 b}$

Step 3

Factor out negative.

$\frac{4 a^{6} b^{8}}{- a^{3} b}$

Step 4

Cancel the common factor of $a^{6}$ and $a^{3}$ .

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Step 4.1

Factor $a^{3}$ out of $4 a^{6} b^{8}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

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

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Step 5.1

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

$\frac{b (4 a^{3} b^{7})}{- 1 b}$

Step 5.2

Move the negative one from the denominator of $\frac{4 a^{3} b^{7}}{- 1}$ .

$- 1 \cdot (4 a^{3} b^{7})$

Step 6

Simplify the expression.

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Step 6.1

Rewrite $- 1 \cdot (4 a^{3} b^{7})$ as $- (4 a^{3} b^{7})$ .

$- (4 a^{3} b^{7})$

Step 6.2

Multiply $4$ by $- 1$ .

$- 4 a^{3} b^{7}$