Finite Math Examples

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

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

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

Step 1.2

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

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

Step 2

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

$25 {(a^{6})}^{2} {(b^{3})}^{2}$

Step 3

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

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Step 3.1

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

$25 a^{6 \cdot 2} {(b^{3})}^{2}$

Step 3.2

Multiply $6$ by $2$ .

$25 a^{12} {(b^{3})}^{2}$

Step 4

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

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Step 4.1

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

$25 a^{12} b^{3 \cdot 2}$

Step 4.2

Multiply $3$ by $2$ .

$25 a^{12} b^{6}$