Pre-Algebra Examples

$\frac{- 21 a^{9} b^{- 8} c^{3}}{- 7 a^{- 8} b^{- 7} c^{- 4}}$

Step 1

Move $b^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 21 a^{9} c^{3}}{- 7 a^{- 8} b^{- 7} c^{- 4} b^{8}}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $b^{- 7}$ by $b^{8}$ by adding the exponents.

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Step 2.1.1

Move $b^{8}$ .

$\frac{- 21 a^{9} c^{3}}{- 7 a^{- 8} (b^{8} b^{- 7}) c^{- 4}}$

Step 2.1.2

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

$\frac{- 21 a^{9} c^{3}}{- 7 a^{- 8} b^{8 - 7} c^{- 4}}$

Step 2.1.3

Subtract $7$ from $8$ .

$\frac{- 21 a^{9} c^{3}}{- 7 a^{- 8} b^{1} c^{- 4}}$

Step 2.2

Simplify $- 7 a^{- 8} b^{1} c^{- 4}$ .

$\frac{- 21 a^{9} c^{3}}{- 7 a^{- 8} b c^{- 4}}$

Step 3

Move $a^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 21 a^{9} c^{3} a^{8}}{- 7 b c^{- 4}}$

Step 4

Move $c^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 21 a^{9} c^{3} a^{8} c^{4}}{- 7 b}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $a^{9}$ by $a^{8}$ by adding the exponents.

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Step 5.1.1

Move $a^{8}$ .

$\frac{- 21 (a^{8} a^{9}) c^{3} c^{4}}{- 7 b}$

Step 5.1.2

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

$\frac{- 21 a^{8 + 9} c^{3} c^{4}}{- 7 b}$

Step 5.1.3

Add $8$ and $9$ .

$\frac{- 21 a^{17} c^{3} c^{4}}{- 7 b}$

Step 5.2

Multiply $c^{3}$ by $c^{4}$ by adding the exponents.

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Step 5.2.1

Move $c^{4}$ .

$\frac{- 21 a^{17} (c^{4} c^{3})}{- 7 b}$

Step 5.2.2

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

$\frac{- 21 a^{17} c^{4 + 3}}{- 7 b}$

Step 5.2.3

Add $4$ and $3$ .

$\frac{- 21 a^{17} c^{7}}{- 7 b}$

Step 6

Cancel the common factor of $- 21$ and $- 7$ .

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Step 6.1

Factor $- 7$ out of $- 21 a^{17} c^{7}$ .

$\frac{- 7 (3 a^{17} c^{7})}{- 7 b}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $- 7$ out of $- 7 b$ .

$\frac{- 7 (3 a^{17} c^{7})}{- 7 (b)}$

Step 6.2.2

Cancel the common factor.

$\frac{- 7 (3 a^{17} c^{7})}{- 7 b}$

Step 6.2.3

Rewrite the expression.

$\frac{3 a^{17} c^{7}}{b}$