Basic Math Examples

$\frac{- 56 a^{- 2} b^{- 3}}{7 {(a b)}^{- 7}}$

Step 1

Simplify.

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Step 1.1

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

$\frac{- 56 b^{- 3}}{7 {(a b)}^{- 7} a^{2}}$

Step 1.2

Move $b^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 56}{7 {(a b)}^{- 7} a^{2} b^{3}}$

Step 1.3

Move ${(a b)}^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 56 {(a b)}^{7}}{7 a^{2} b^{3}}$

Step 2

Cancel the common factor of $- 56$ and $7$ .

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Step 2.1

Factor $7$ out of $- 56 {(a b)}^{7}$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Apply the product rule to $a b$ .

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

Step 4

Cancel the common factor of $a^{7}$ and $a^{2}$ .

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Step 4.1

Factor $a^{2}$ out of $- 8 a^{7} b^{7}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

$\frac{- 8 a^{5} b^{7}}{b^{3}}$

Step 5

Cancel the common factor of $b^{7}$ and $b^{3}$ .

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Step 5.1

Factor $b^{3}$ out of $- 8 a^{5} b^{7}$ .

$\frac{b^{3} (- 8 a^{5} b^{4})}{b^{3}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Multiply by $1$ .

$\frac{b^{3} (- 8 a^{5} b^{4})}{b^{3} \cdot 1}$

Step 5.2.2

Cancel the common factor.

$\frac{b^{3} (- 8 a^{5} b^{4})}{b^{3} \cdot 1}$

Step 5.2.3

Rewrite the expression.

$\frac{- 8 a^{5} b^{4}}{1}$

Step 5.2.4

Divide $- 8 a^{5} b^{4}$ by $1$ .

$- 8 a^{5} b^{4}$