Basic Math Examples

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

Step 1

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

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

Step 2

Rewrite using the commutative property of multiplication.

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

Step 3

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

$27 z {(z^{2})}^{3}$

Step 4

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

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Step 4.1

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

$27 z \cdot z^{2 \cdot 3}$

Step 4.2

Multiply $2$ by $3$ .

$27 z \cdot z^{6}$

Step 5

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

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Step 5.1

Move $z^{6}$ .

$27 (z^{6} z)$

Step 5.2

Multiply $z^{6}$ by $z$ .

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Step 5.2.1

Raise $z$ to the power of $1$ .

$27 (z^{6} z^{1})$

Step 5.2.2

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

$27 z^{6 + 1}$

Step 5.3

Add $6$ and $1$ .

$27 z^{7}$