Basic Math Examples

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

Step 1

Multiply $z^{4}$ by $z^{- 2}$ by adding the exponents.

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Step 1.1

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

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

Step 1.2

Subtract $2$ from $4$ .

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

Step 2

Move ${(z^{4})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{z^{2} {(z^{4})}^{3}}$

Step 3

Multiply the exponents in ${(z^{4})}^{3}$ .

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Step 3.1

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

$\frac{1}{z^{2} z^{4 \cdot 3}}$

Step 3.2

Multiply $4$ by $3$ .

$\frac{1}{z^{2} z^{12}}$

Step 4

Multiply $z^{2}$ by $z^{12}$ by adding the exponents.

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Step 4.1

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

$\frac{1}{z^{2 + 12}}$

Step 4.2

Add $2$ and $12$ .

$\frac{1}{z^{14}}$