Precalculus Examples

${(- 5 z^{2})}^{3} (4 z^{3})$

Step 1

Rewrite using the commutative property of multiplication.

$4 {(- 5 z^{2})}^{3} z^{3}$

Step 2

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

$4 ({(- 5)}^{3} {(z^{2})}^{3}) z^{3}$

Step 3

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

$4 (- 125 {(z^{2})}^{3}) z^{3}$

Step 4

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

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Step 4.1

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

$4 (- 125 z^{2 \cdot 3}) z^{3}$

Step 4.2

Multiply $2$ by $3$ .

$4 (- 125 z^{6}) z^{3}$

Step 5

Multiply $z^{6}$ by $z^{3}$ by adding the exponents.

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Step 5.1

Move $z^{3}$ .

$4 (- 125 (z^{3} z^{6}))$

Step 5.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 (- 125 z^{3 + 6})$

Step 5.3

Add $3$ and $6$ .

$4 (- 125 z^{9})$

Step 6

Multiply $- 125$ by $4$ .

$- 500 z^{9}$