Basic Math Examples

$(3 c^{5} d^{4} - 6 c^{2}) (- 9 c d^{6})$

Step 1

Apply the distributive property.

$3 c^{5} d^{4} (- 9 c d^{6}) - 6 c^{2} (- 9 c d^{6})$

Step 2

Multiply $c^{5}$ by $c$ by adding the exponents.

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Step 2.1

Move $c$ .

$3 (c \cdot c^{5}) d^{4} (- 9 d^{6}) - 6 c^{2} (- 9 c d^{6})$

Step 2.2

Multiply $c$ by $c^{5}$ .

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Step 2.2.1

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

$3 (c^{1} c^{5}) d^{4} (- 9 d^{6}) - 6 c^{2} (- 9 c d^{6})$

Step 2.2.2

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

$3 c^{1 + 5} d^{4} (- 9 d^{6}) - 6 c^{2} (- 9 c d^{6})$

Step 2.3

Add $1$ and $5$ .

$3 c^{6} d^{4} (- 9 d^{6}) - 6 c^{2} (- 9 c d^{6})$

Step 3

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

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Step 3.1

Move $c$ .

$3 c^{6} d^{4} (- 9 d^{6}) - 6 (c \cdot c^{2}) (- 9 d^{6})$

Step 3.2

Multiply $c$ by $c^{2}$ .

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Step 3.2.1

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

$3 c^{6} d^{4} (- 9 d^{6}) - 6 (c^{1} c^{2}) (- 9 d^{6})$

Step 3.2.2

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

$3 c^{6} d^{4} (- 9 d^{6}) - 6 c^{1 + 2} (- 9 d^{6})$

Step 3.3

Add $1$ and $2$ .

$3 c^{6} d^{4} (- 9 d^{6}) - 6 c^{3} (- 9 d^{6})$

Step 4

Simplify each term.

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Step 4.1

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

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Step 4.1.1

Move $d^{6}$ .

$3 c^{6} (d^{6} d^{4}) \cdot - 9 - 6 c^{3} (- 9 d^{6})$

Step 4.1.2

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

$3 c^{6} d^{6 + 4} \cdot - 9 - 6 c^{3} (- 9 d^{6})$

Step 4.1.3

Add $6$ and $4$ .

$3 c^{6} d^{10} \cdot - 9 - 6 c^{3} (- 9 d^{6})$

Step 4.2

Multiply $- 9$ by $3$ .

$- 27 c^{6} d^{10} - 6 c^{3} (- 9 d^{6})$

Step 4.3

Rewrite using the commutative property of multiplication.

$- 27 c^{6} d^{10} - 6 \cdot - 9 c^{3} d^{6}$

Step 4.4

Multiply $- 6$ by $- 9$ .

$- 27 c^{6} d^{10} + 54 c^{3} d^{6}$