Basic Math Examples

${(- a^{3} b^{5} c)}^{4}$

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

${(- a^{3} b^{5})}^{4} c^{4}$

Step 1.2

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

${(- a^{3})}^{4} {(b^{5})}^{4} c^{4}$

Step 1.3

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

${(- 1)}^{4} {(a^{3})}^{4} {(b^{5})}^{4} c^{4}$

Step 2

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

$1 {(a^{3})}^{4} {(b^{5})}^{4} c^{4}$

Step 3

Multiply ${(a^{3})}^{4}$ by $1$ .

${(a^{3})}^{4} {(b^{5})}^{4} c^{4}$

Step 4

Multiply the exponents in ${(a^{3})}^{4}$ .

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Step 4.1

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

$a^{3 \cdot 4} {(b^{5})}^{4} c^{4}$

Step 4.2

Multiply $3$ by $4$ .

$a^{12} {(b^{5})}^{4} c^{4}$

Step 5

Multiply the exponents in ${(b^{5})}^{4}$ .

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Step 5.1

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

$a^{12} b^{5 \cdot 4} c^{4}$

Step 5.2

Multiply $5$ by $4$ .

$a^{12} b^{20} c^{4}$