Finite Math Examples

${(- 5 a^{2} b^{4} c^{0})}^{2}$

Step 1

Anything raised to $0$ is $1$ .

${(- 5 a^{2} b^{4} \cdot 1)}^{2}$

Step 2

Multiply $- 5$ by $1$ .

${(- 5 a^{2} b^{4})}^{2}$

Step 3

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

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Step 3.1

Apply the product rule to $- 5 a^{2} b^{4}$ .

${(- 5 a^{2})}^{2} {(b^{4})}^{2}$

Step 3.2

Apply the product rule to $- 5 a^{2}$ .

${(- 5)}^{2} {(a^{2})}^{2} {(b^{4})}^{2}$

Step 4

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

$25 {(a^{2})}^{2} {(b^{4})}^{2}$

Step 5

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

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Step 5.1

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

$25 a^{2 \cdot 2} {(b^{4})}^{2}$

Step 5.2

Multiply $2$ by $2$ .

$25 a^{4} {(b^{4})}^{2}$

Step 6

Multiply the exponents in ${(b^{4})}^{2}$ .

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Step 6.1

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

$25 a^{4} b^{4 \cdot 2}$

Step 6.2

Multiply $4$ by $2$ .

$25 a^{4} b^{8}$