Precalculus Examples

${(- 5 c^{2} d^{5})}^{3}$

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 $- 5 c^{2} d^{5}$ .

${(- 5 c^{2})}^{3} {(d^{5})}^{3}$

Step 1.2

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

${(- 5)}^{3} {(c^{2})}^{3} {(d^{5})}^{3}$

Step 2

Raise $- 5$ to the power of $3$ .

$- 125 {(c^{2})}^{3} {(d^{5})}^{3}$

Step 3

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

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Step 3.1

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

$- 125 c^{2 \cdot 3} {(d^{5})}^{3}$

Step 3.2

Multiply $2$ by $3$ .

$- 125 c^{6} {(d^{5})}^{3}$

Step 4

Multiply the exponents in ${(d^{5})}^{3}$ .

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Step 4.1

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

$- 125 c^{6} d^{5 \cdot 3}$

Step 4.2

Multiply $5$ by $3$ .

$- 125 c^{6} d^{15}$