Algebra Examples

$7 a^{4} b \cdot {(- 3 a^{5} b^{6})}^{2}$

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 $- 3 a^{5} b^{6}$ .

$7 a^{4} b \cdot ({(- 3 a^{5})}^{2} {(b^{6})}^{2})$

Step 1.2

Apply the product rule to $- 3 a^{5}$ .

$7 a^{4} b \cdot ({(- 3)}^{2} {(a^{5})}^{2} {(b^{6})}^{2})$

Step 2

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

$7 a^{4} b \cdot (9 {(a^{5})}^{2} {(b^{6})}^{2})$

Step 3

Multiply the exponents in ${(a^{5})}^{2}$ .

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Step 3.1

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

$7 a^{4} b \cdot (9 a^{5 \cdot 2} {(b^{6})}^{2})$

Step 3.2

Multiply $5$ by $2$ .

$7 a^{4} b \cdot (9 a^{10} {(b^{6})}^{2})$

Step 4

Multiply $a^{4}$ by $a^{10}$ by adding the exponents.

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Step 4.1

Move $a^{10}$ .

$7 (a^{10} a^{4}) b \cdot (9 {(b^{6})}^{2})$

Step 4.2

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

$7 a^{10 + 4} b \cdot (9 {(b^{6})}^{2})$

Step 4.3

Add $10$ and $4$ .

$7 a^{14} b \cdot (9 {(b^{6})}^{2})$

Step 5

Multiply the exponents in ${(b^{6})}^{2}$ .

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Step 5.1

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

$7 a^{14} b \cdot (9 b^{6 \cdot 2})$

Step 5.2

Multiply $6$ by $2$ .

$7 a^{14} b \cdot (9 b^{12})$

Step 6

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

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Step 6.1

Move $b^{12}$ .

$7 a^{14} (b^{12} b) \cdot 9$

Step 6.2

Multiply $b^{12}$ by $b$ .

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Step 6.2.1

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

$7 a^{14} (b^{12} b^{1}) \cdot 9$

Step 6.2.2

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

$7 a^{14} b^{12 + 1} \cdot 9$

Step 6.3

Add $12$ and $1$ .

$7 a^{14} b^{13} \cdot 9$

Step 7

Multiply $9$ by $7$ .

$63 a^{14} b^{13}$