Algebra Examples

$(a^{- 5} b^{8} c^{- 12}) (a^{7} b^{- 3} c^{7})$

Step 1

Multiply $a^{- 5}$ by $a^{7}$ by adding the exponents.

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Step 1.1

Move $a^{7}$ .

$a^{7} a^{- 5} b^{8} c^{- 12} (b^{- 3} c^{7})$

Step 1.2

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

$a^{7 - 5} b^{8} c^{- 12} (b^{- 3} c^{7})$

Step 1.3

Subtract $5$ from $7$ .

$a^{2} b^{8} c^{- 12} (b^{- 3} c^{7})$

Step 2

Multiply $b^{8}$ by $b^{- 3}$ by adding the exponents.

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Step 2.1

Move $b^{- 3}$ .

$a^{2} (b^{- 3} b^{8}) c^{- 12} c^{7}$

Step 2.2

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

$a^{2} b^{- 3 + 8} c^{- 12} c^{7}$

Step 2.3

Add $- 3$ and $8$ .

$a^{2} b^{5} c^{- 12} c^{7}$

Step 3

Multiply $c^{- 12}$ by $c^{7}$ by adding the exponents.

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Step 3.1

Move $c^{7}$ .

$a^{2} b^{5} (c^{7} c^{- 12})$

Step 3.2

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

$a^{2} b^{5} c^{7 - 12}$

Step 3.3

Subtract $12$ from $7$ .

$a^{2} b^{5} c^{- 5}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$a^{2} b^{5} \frac{1}{c^{5}}$

Step 5

Multiply $a^{2} b^{5} \frac{1}{c^{5}}$ .

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Step 5.1

Combine $a^{2}$ and $\frac{1}{c^{5}}$ .

$b^{5} \frac{a^{2}}{c^{5}}$

Step 5.2

Combine $b^{5}$ and $\frac{a^{2}}{c^{5}}$ .

$\frac{b^{5} a^{2}}{c^{5}}$