Algebra Examples

$\frac{a^{2} b^{- 4} c^{3} d^{- 2}}{a^{- 3} b^{2} c^{- 4} d^{- 4}}$

Step 1

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

$\frac{a^{2} c^{3} d^{- 2}}{a^{- 3} b^{2} c^{- 4} d^{- 4} b^{4}}$

Step 2

Multiply $b^{2}$ by $b^{4}$ by adding the exponents.

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Step 2.1

Move $b^{4}$ .

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

Step 2.2

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

$\frac{a^{2} c^{3} d^{- 2}}{a^{- 3} b^{4 + 2} c^{- 4} d^{- 4}}$

Step 2.3

Add $4$ and $2$ .

$\frac{a^{2} c^{3} d^{- 2}}{a^{- 3} b^{6} c^{- 4} d^{- 4}}$

Step 3

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

$\frac{a^{2} c^{3} d^{- 2} a^{3}}{b^{6} c^{- 4} d^{- 4}}$

Step 4

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

$\frac{a^{2} c^{3} d^{- 2} a^{3} c^{4}}{b^{6} d^{- 4}}$

Step 5

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

$\frac{a^{2} c^{3} d^{- 2} a^{3} c^{4} d^{4}}{b^{6}}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $a^{2}$ by $a^{3}$ by adding the exponents.

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Step 6.1.1

Move $a^{3}$ .

$\frac{a^{3} a^{2} c^{3} d^{- 2} c^{4} d^{4}}{b^{6}}$

Step 6.1.2

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

$\frac{a^{3 + 2} c^{3} d^{- 2} c^{4} d^{4}}{b^{6}}$

Step 6.1.3

Add $3$ and $2$ .

$\frac{a^{5} c^{3} d^{- 2} c^{4} d^{4}}{b^{6}}$

Step 6.2

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

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Step 6.2.1

Move $c^{4}$ .

$\frac{a^{5} (c^{4} c^{3}) d^{- 2} d^{4}}{b^{6}}$

Step 6.2.2

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

$\frac{a^{5} c^{4 + 3} d^{- 2} d^{4}}{b^{6}}$

Step 6.2.3

Add $4$ and $3$ .

$\frac{a^{5} c^{7} d^{- 2} d^{4}}{b^{6}}$

Step 6.3

Multiply $d^{- 2}$ by $d^{4}$ by adding the exponents.

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Step 6.3.1

Move $d^{4}$ .

$\frac{a^{5} c^{7} (d^{4} d^{- 2})}{b^{6}}$

Step 6.3.2

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

$\frac{a^{5} c^{7} d^{4 - 2}}{b^{6}}$

Step 6.3.3

Subtract $2$ from $4$ .

$\frac{a^{5} c^{7} d^{2}}{b^{6}}$