Pre-Algebra Examples

$\frac{7 a^{4} b^{- 5} c^{2} d}{28 a^{2} b^{- 2} c^{- 4} e^{- 2}}$

Step 1

Move $b^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{7 a^{4} c^{2} d}{28 a^{2} b^{- 2} c^{- 4} e^{- 2} b^{5}}$

Step 2

Multiply $b^{- 2}$ by $b^{5}$ by adding the exponents.

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Step 2.1

Move $b^{5}$ .

$\frac{7 a^{4} c^{2} d}{28 a^{2} (b^{5} b^{- 2}) c^{- 4} e^{- 2}}$

Step 2.2

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

$\frac{7 a^{4} c^{2} d}{28 a^{2} b^{5 - 2} c^{- 4} e^{- 2}}$

Step 2.3

Subtract $2$ from $5$ .

$\frac{7 a^{4} c^{2} d}{28 a^{2} b^{3} c^{- 4} e^{- 2}}$

Step 3

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

$\frac{7 a^{4} c^{2} d c^{4}}{28 a^{2} b^{3} e^{- 2}}$

Step 4

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

$\frac{7 a^{4} c^{2} d c^{4} e^{2}}{28 a^{2} b^{3}}$

Step 5

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

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Step 5.1

Move $c^{4}$ .

$\frac{7 a^{4} (c^{4} c^{2}) d e^{2}}{28 a^{2} b^{3}}$

Step 5.2

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

$\frac{7 a^{4} c^{4 + 2} d e^{2}}{28 a^{2} b^{3}}$

Step 5.3

Add $4$ and $2$ .

$\frac{7 a^{4} c^{6} d e^{2}}{28 a^{2} b^{3}}$

Step 6

Cancel the common factor of $7$ and $28$ .

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Step 6.1

Factor $7$ out of $7 a^{4} c^{6} d e^{2}$ .

$\frac{7 (a^{4} c^{6} d e^{2})}{28 a^{2} b^{3}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $7$ out of $28 a^{2} b^{3}$ .

$\frac{7 (a^{4} c^{6} d e^{2})}{7 (4 a^{2} b^{3})}$

Step 6.2.2

Cancel the common factor.

$\frac{7 (a^{4} c^{6} d e^{2})}{7 (4 a^{2} b^{3})}$

Step 6.2.3

Rewrite the expression.

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

Step 7

Cancel the common factor of $a^{4}$ and $a^{2}$ .

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Step 7.1

Factor $a^{2}$ out of $a^{4} c^{6} d e^{2}$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $a^{2}$ out of $4 a^{2} b^{3}$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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