Pre-Algebra Examples

${(- 6 a^{5} b^{3} c)}^{2}$

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

${(- 6 a^{5} b^{3})}^{2} c^{2}$

Step 1.2

Apply the product rule to $- 6 a^{5} b^{3}$ .

${(- 6 a^{5})}^{2} {(b^{3})}^{2} c^{2}$

Step 1.3

Apply the product rule to $- 6 a^{5}$ .

${(- 6)}^{2} {(a^{5})}^{2} {(b^{3})}^{2} c^{2}$

Step 2

Raise $- 6$ to the power of $2$ .

$36 {(a^{5})}^{2} {(b^{3})}^{2} c^{2}$

Step 3

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

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Step 3.1

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

$36 a^{5 \cdot 2} {(b^{3})}^{2} c^{2}$

Step 3.2

Multiply $5$ by $2$ .

$36 a^{10} {(b^{3})}^{2} c^{2}$

Step 4

Multiply the exponents in ${(b^{3})}^{2}$ .

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Step 4.1

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

$36 a^{10} b^{3 \cdot 2} c^{2}$

Step 4.2

Multiply $3$ by $2$ .

$36 a^{10} b^{6} c^{2}$