Basic Math Examples

$- 2 {(- 2 a^{9} b^{4})}^{3} {(3 a^{9} b)}^{2}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $- 2 a^{9} b^{4}$ .

$- 2 ({(- 2 a^{9})}^{3} {(b^{4})}^{3}) {(3 a^{9} b)}^{2}$

Step 1.2

Apply the product rule to $- 2 a^{9}$ .

$- 2 ({(- 2)}^{3} {(a^{9})}^{3} {(b^{4})}^{3}) {(3 a^{9} b)}^{2}$

Step 2

Multiply $- 2$ by ${(- 2)}^{3}$ by adding the exponents.

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Step 2.1

Move ${(- 2)}^{3}$ .

${(- 2)}^{3} \cdot - 2 ({(a^{9})}^{3} {(b^{4})}^{3}) {(3 a^{9} b)}^{2}$

Step 2.2

Multiply ${(- 2)}^{3}$ by $- 2$ .

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Step 2.2.1

Raise $- 2$ to the power of $1$ .

${(- 2)}^{3} \cdot {(- 2)}^{1} ({(a^{9})}^{3} {(b^{4})}^{3}) {(3 a^{9} b)}^{2}$

Step 2.2.2

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

${(- 2)}^{3 + 1} ({(a^{9})}^{3} {(b^{4})}^{3}) {(3 a^{9} b)}^{2}$

Step 2.3

Add $3$ and $1$ .

${(- 2)}^{4} ({(a^{9})}^{3} {(b^{4})}^{3}) {(3 a^{9} b)}^{2}$

Step 3

Raise $- 2$ to the power of $4$ .

$16 ({(a^{9})}^{3} {(b^{4})}^{3}) {(3 a^{9} b)}^{2}$

Step 4

Multiply the exponents in ${(a^{9})}^{3}$ .

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Step 4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$16 (a^{9 \cdot 3} {(b^{4})}^{3}) {(3 a^{9} b)}^{2}$

Step 4.2

Multiply $9$ by $3$ .

$16 (a^{27} {(b^{4})}^{3}) {(3 a^{9} b)}^{2}$

Step 5

Multiply the exponents in ${(b^{4})}^{3}$ .

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Step 5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$16 (a^{27} b^{4 \cdot 3}) {(3 a^{9} b)}^{2}$

Step 5.2

Multiply $4$ by $3$ .

$16 (a^{27} b^{12}) {(3 a^{9} b)}^{2}$

Step 6

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 6.1

Apply the product rule to $3 a^{9} b$ .

$16 a^{27} b^{12} ({(3 a^{9})}^{2} b^{2})$

Step 6.2

Apply the product rule to $3 a^{9}$ .

$16 a^{27} b^{12} (3^{2} {(a^{9})}^{2} b^{2})$

Step 7

Multiply $b^{12}$ by $b^{2}$ by adding the exponents.

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Step 7.1

Move $b^{2}$ .

$16 a^{27} (b^{2} b^{12}) (3^{2} {(a^{9})}^{2})$

Step 7.2

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

$16 a^{27} b^{2 + 12} (3^{2} {(a^{9})}^{2})$

Step 7.3

Add $2$ and $12$ .

$16 a^{27} b^{14} (3^{2} {(a^{9})}^{2})$

Step 8

Raise $3$ to the power of $2$ .

$16 a^{27} b^{14} (9 {(a^{9})}^{2})$

Step 9

Multiply the exponents in ${(a^{9})}^{2}$ .

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Step 9.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$16 a^{27} b^{14} (9 a^{9 \cdot 2})$

Step 9.2

Multiply $9$ by $2$ .

$16 a^{27} b^{14} (9 a^{18})$

Step 10

Multiply $a^{27}$ by $a^{18}$ by adding the exponents.

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Step 10.1

Move $a^{18}$ .

$16 (a^{18} a^{27}) b^{14} \cdot 9$

Step 10.2

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

$16 a^{18 + 27} b^{14} \cdot 9$

Step 10.3

Add $18$ and $27$ .

$16 a^{45} b^{14} \cdot 9$

Step 11

Multiply $9$ by $16$ .

$144 a^{45} b^{14}$