Algebra Examples

${(- a^{6} b)}^{2} + 9 a^{12} b^{2}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Apply the product rule to $- a^{6} b$ .

${(- a^{6})}^{2} b^{2} + 9 a^{12} b^{2}$

Step 1.1.2

Apply the product rule to $- a^{6}$ .

${(- 1)}^{2} {(a^{6})}^{2} b^{2} + 9 a^{12} b^{2}$

Step 1.2

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

$1 {(a^{6})}^{2} b^{2} + 9 a^{12} b^{2}$

Step 1.3

Multiply ${(a^{6})}^{2}$ by $1$ .

${(a^{6})}^{2} b^{2} + 9 a^{12} b^{2}$

Step 1.4

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

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Step 1.4.1

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

$a^{6 \cdot 2} b^{2} + 9 a^{12} b^{2}$

Step 1.4.2

Multiply $6$ by $2$ .

$a^{12} b^{2} + 9 a^{12} b^{2}$

Step 2

Add $a^{12} b^{2}$ and $9 a^{12} b^{2}$ .

$10 a^{12} b^{2}$