Basic Math Examples

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

Step 1

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

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Step 1.1

Multiply $z$ by $z^{2}$ .

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Step 1.1.1

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

$z^{1} \cdot z^{2} \cdot z^{- 3}$

Step 1.1.2

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

$z^{1 + 2} \cdot z^{- 3}$

Step 1.2

Add $1$ and $2$ .

$z^{3} \cdot z^{- 3}$

Step 2

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

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Step 2.1

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

$z^{3 - 3}$

Step 2.2

Subtract $3$ from $3$ .

$z^{0}$

Step 3

Simplify $z^{0}$ .

$1$