Algebra Examples

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

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 $- a^{9} b$ .

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

Step 1.2

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

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

Step 2

Raise $- 1$ to the power of $4$ .

$1 {(a^{9})}^{4} b^{4}$

Step 3

Multiply ${(a^{9})}^{4}$ by $1$ .

${(a^{9})}^{4} b^{4}$

Step 4

Multiply the exponents in ${(a^{9})}^{4}$ .

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Step 4.1

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

$a^{9 \cdot 4} b^{4}$

Step 4.2

Multiply $9$ by $4$ .

$a^{36} b^{4}$