Pre-Algebra Examples

$9 a^{3} x^{7} (- 11 a^{6} x^{9} + 12 x^{6} - 3 a)$

Step 1

Apply the distributive property.

$9 a^{3} x^{7} (- 11 a^{6} x^{9}) + 9 a^{3} x^{7} (12 x^{6}) + 9 a^{3} x^{7} (- 3 a)$

Step 2

Simplify.

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Step 2.1

Multiply $a^{3}$ by $a^{6}$ by adding the exponents.

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Step 2.1.1

Move $a^{6}$ .

$9 (a^{6} a^{3}) x^{7} (- 11 x^{9}) + 9 a^{3} x^{7} (12 x^{6}) + 9 a^{3} x^{7} (- 3 a)$

Step 2.1.2

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

$9 a^{6 + 3} x^{7} (- 11 x^{9}) + 9 a^{3} x^{7} (12 x^{6}) + 9 a^{3} x^{7} (- 3 a)$

Step 2.1.3

Add $6$ and $3$ .

$9 a^{9} x^{7} (- 11 x^{9}) + 9 a^{3} x^{7} (12 x^{6}) + 9 a^{3} x^{7} (- 3 a)$

Step 2.2

Multiply $x^{7}$ by $x^{6}$ by adding the exponents.

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Step 2.2.1

Move $x^{6}$ .

$9 a^{9} x^{7} (- 11 x^{9}) + 9 a^{3} (x^{6} x^{7}) \cdot 12 + 9 a^{3} x^{7} (- 3 a)$

Step 2.2.2

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

$9 a^{9} x^{7} (- 11 x^{9}) + 9 a^{3} x^{6 + 7} \cdot 12 + 9 a^{3} x^{7} (- 3 a)$

Step 2.2.3

Add $6$ and $7$ .

$9 a^{9} x^{7} (- 11 x^{9}) + 9 a^{3} x^{13} \cdot 12 + 9 a^{3} x^{7} (- 3 a)$

Step 2.3

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

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Step 2.3.1

Move $a$ .

$9 a^{9} x^{7} (- 11 x^{9}) + 9 a^{3} x^{13} \cdot 12 + 9 (a \cdot a^{3}) x^{7} \cdot - 3$

Step 2.3.2

Multiply $a$ by $a^{3}$ .

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Step 2.3.2.1

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

$9 a^{9} x^{7} (- 11 x^{9}) + 9 a^{3} x^{13} \cdot 12 + 9 (a^{1} a^{3}) x^{7} \cdot - 3$

Step 2.3.2.2

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

$9 a^{9} x^{7} (- 11 x^{9}) + 9 a^{3} x^{13} \cdot 12 + 9 a^{1 + 3} x^{7} \cdot - 3$

Step 2.3.3

Add $1$ and $3$ .

$9 a^{9} x^{7} (- 11 x^{9}) + 9 a^{3} x^{13} \cdot 12 + 9 a^{4} x^{7} \cdot - 3$

Step 3

Simplify each term.

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Step 3.1

Multiply $x^{7}$ by $x^{9}$ by adding the exponents.

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Step 3.1.1

Move $x^{9}$ .

$9 a^{9} (x^{9} x^{7}) \cdot - 11 + 9 a^{3} x^{13} \cdot 12 + 9 a^{4} x^{7} \cdot - 3$

Step 3.1.2

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

$9 a^{9} x^{9 + 7} \cdot - 11 + 9 a^{3} x^{13} \cdot 12 + 9 a^{4} x^{7} \cdot - 3$

Step 3.1.3

Add $9$ and $7$ .

$9 a^{9} x^{16} \cdot - 11 + 9 a^{3} x^{13} \cdot 12 + 9 a^{4} x^{7} \cdot - 3$

Step 3.2

Multiply $- 11$ by $9$ .

$- 99 a^{9} x^{16} + 9 a^{3} x^{13} \cdot 12 + 9 a^{4} x^{7} \cdot - 3$

Step 3.3

Multiply $12$ by $9$ .

$- 99 a^{9} x^{16} + 108 a^{3} x^{13} + 9 a^{4} x^{7} \cdot - 3$

Step 3.4

Multiply $- 3$ by $9$ .

$- 99 a^{9} x^{16} + 108 a^{3} x^{13} - 27 a^{4} x^{7}$