Pre-Algebra Examples

${(- 2 a b^{2})}^{5}$

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 $- 2 a b^{2}$ .

${(- 2 a)}^{5} {(b^{2})}^{5}$

Step 1.2

Apply the product rule to $- 2 a$ .

${(- 2)}^{5} a^{5} {(b^{2})}^{5}$

Step 2

Raise $- 2$ to the power of $5$ .

$- 32 a^{5} {(b^{2})}^{5}$

Step 3

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

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Step 3.1

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

$- 32 a^{5} b^{2 \cdot 5}$

Step 3.2

Multiply $2$ by $5$ .

$- 32 a^{5} b^{10}$