Precalculus Examples

$3 z^{2} {(2 z^{3})}^{2}$

Step 1

Apply the product rule to $2 z^{3}$ .

$3 z^{2} (2^{2} {(z^{3})}^{2})$

Step 2

Rewrite using the commutative property of multiplication.

$3 \cdot 2^{2} z^{2} {(z^{3})}^{2}$

Step 3

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

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

Step 4

Multiply $3$ by $4$ .

$12 z^{2} {(z^{3})}^{2}$

Step 5

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

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Step 5.1

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

$12 z^{2} z^{3 \cdot 2}$

Step 5.2

Multiply $3$ by $2$ .

$12 z^{2} z^{6}$

Step 6

Multiply $z^{2}$ by $z^{6}$ by adding the exponents.

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Step 6.1

Move $z^{6}$ .

$12 (z^{6} z^{2})$

Step 6.2

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

$12 z^{6 + 2}$

Step 6.3

Add $6$ and $2$ .

$12 z^{8}$