Pre-Algebra Examples

$\frac{21 c^{10} g^{11} - 6 c^{8} g^{9} + 15 c^{4} g^{5}}{3 c^{4} g}$

Step 1

Factor $3 c^{4} g^{5}$ out of $21 c^{10} g^{11} - 6 c^{8} g^{9} + 15 c^{4} g^{5}$ .

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Step 1.1

Factor $3 c^{4} g^{5}$ out of $21 c^{10} g^{11}$ .

$\frac{3 c^{4} g^{5} (7 c^{6} g^{6}) - 6 c^{8} g^{9} + 15 c^{4} g^{5}}{3 c^{4} g}$

Step 1.2

Factor $3 c^{4} g^{5}$ out of $- 6 c^{8} g^{9}$ .

$\frac{3 c^{4} g^{5} (7 c^{6} g^{6}) + 3 c^{4} g^{5} (- 2 c^{4} g^{4}) + 15 c^{4} g^{5}}{3 c^{4} g}$

Step 1.3

Factor $3 c^{4} g^{5}$ out of $15 c^{4} g^{5}$ .

$\frac{3 c^{4} g^{5} (7 c^{6} g^{6}) + 3 c^{4} g^{5} (- 2 c^{4} g^{4}) + 3 c^{4} g^{5} (5)}{3 c^{4} g}$

Step 1.4

Factor $3 c^{4} g^{5}$ out of $3 c^{4} g^{5} (7 c^{6} g^{6}) + 3 c^{4} g^{5} (- 2 c^{4} g^{4})$ .

$\frac{3 c^{4} g^{5} (7 c^{6} g^{6} - 2 c^{4} g^{4}) + 3 c^{4} g^{5} (5)}{3 c^{4} g}$

Step 1.5

Factor $3 c^{4} g^{5}$ out of $3 c^{4} g^{5} (7 c^{6} g^{6} - 2 c^{4} g^{4}) + 3 c^{4} g^{5} (5)$ .

$\frac{3 c^{4} g^{5} (7 c^{6} g^{6} - 2 c^{4} g^{4} + 5)}{3 c^{4} g}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$\frac{3 c^{4} g^{5} (7 c^{6} g^{6} - 2 c^{4} g^{4} + 5)}{3 c^{4} g}$

Step 2.2

Rewrite the expression.

$\frac{c^{4} g^{5} (7 c^{6} g^{6} - 2 c^{4} g^{4} + 5)}{c^{4} g}$

Step 3

Cancel the common factor of $c^{4}$ .

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Step 3.1

Cancel the common factor.

$\frac{c^{4} g^{5} (7 c^{6} g^{6} - 2 c^{4} g^{4} + 5)}{c^{4} g}$

Step 3.2

Rewrite the expression.

$\frac{g^{5} (7 c^{6} g^{6} - 2 c^{4} g^{4} + 5)}{g}$

Step 4

Cancel the common factor of $g^{5}$ and $g$ .

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Step 4.1

Factor $g$ out of $g^{5} (7 c^{6} g^{6} - 2 c^{4} g^{4} + 5)$ .

$\frac{g (g^{4} (7 c^{6} g^{6} - 2 c^{4} g^{4} + 5))}{g}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Raise $g$ to the power of $1$ .

$\frac{g (g^{4} (7 c^{6} g^{6} - 2 c^{4} g^{4} + 5))}{g^{1}}$

Step 4.2.2

Factor $g$ out of $g^{1}$ .

$\frac{g (g^{4} (7 c^{6} g^{6} - 2 c^{4} g^{4} + 5))}{g \cdot 1}$

Step 4.2.3

Cancel the common factor.

$\frac{g (g^{4} (7 c^{6} g^{6} - 2 c^{4} g^{4} + 5))}{g \cdot 1}$

Step 4.2.4

Rewrite the expression.

$\frac{g^{4} (7 c^{6} g^{6} - 2 c^{4} g^{4} + 5)}{1}$

Step 4.2.5

Divide $g^{4} (7 c^{6} g^{6} - 2 c^{4} g^{4} + 5)$ by $1$ .

$g^{4} (7 c^{6} g^{6} - 2 c^{4} g^{4} + 5)$

Step 5

Apply the distributive property.

$g^{4} (7 c^{6} g^{6}) + g^{4} (- 2 c^{4} g^{4}) + g^{4} \cdot 5$

Step 6

Simplify.

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Step 6.1

Rewrite using the commutative property of multiplication.

$7 g^{4} (c^{6} g^{6}) + g^{4} (- 2 c^{4} g^{4}) + g^{4} \cdot 5$

Step 6.2

Rewrite using the commutative property of multiplication.

$7 g^{4} (c^{6} g^{6}) - 2 g^{4} (c^{4} g^{4}) + g^{4} \cdot 5$

Step 6.3

Move $5$ to the left of $g^{4}$ .

$7 g^{4} (c^{6} g^{6}) - 2 g^{4} (c^{4} g^{4}) + 5 \cdot g^{4}$

Step 7

Simplify each term.

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Step 7.1

Multiply $g^{4}$ by $g^{6}$ by adding the exponents.

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Step 7.1.1

Move $g^{6}$ .

$7 (g^{6} g^{4}) c^{6} - 2 g^{4} (c^{4} g^{4}) + 5 \cdot g^{4}$

Step 7.1.2

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

$7 g^{6 + 4} c^{6} - 2 g^{4} (c^{4} g^{4}) + 5 \cdot g^{4}$

Step 7.1.3

Add $6$ and $4$ .

$7 g^{10} c^{6} - 2 g^{4} (c^{4} g^{4}) + 5 \cdot g^{4}$

Step 7.2

Multiply $g^{4}$ by $g^{4}$ by adding the exponents.

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Step 7.2.1

Move $g^{4}$ .

$7 g^{10} c^{6} - 2 (g^{4} g^{4}) c^{4} + 5 \cdot g^{4}$

Step 7.2.2

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

$7 g^{10} c^{6} - 2 g^{4 + 4} c^{4} + 5 \cdot g^{4}$

Step 7.2.3

Add $4$ and $4$ .

$7 g^{10} c^{6} - 2 g^{8} c^{4} + 5 \cdot g^{4}$

$7 g^{10} c^{6} - 2 g^{8} c^{4} + 5 g^{4}$