Basic Math Examples

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

Step 1

Multiply $z^{\frac{1}{2}}$ by $z^{- \frac{3}{2}}$ 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.

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

Step 1.2

Combine the numerators over the common denominator.

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

Step 1.3

Subtract $3$ from $1$ .

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

Step 1.4

Divide $- 2$ by $2$ .

$\frac{z^{\frac{1}{3}}}{z^{- 1}}$

Step 2

Move $z^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$z^{\frac{1}{3}} z$

Step 3

Multiply $z^{\frac{1}{3}}$ by $z$ by adding the exponents.

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Step 3.1

Multiply $z^{\frac{1}{3}}$ by $z$ .

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Step 3.1.1

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

$z^{\frac{1}{3}} z^{1}$

Step 3.1.2

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

$z^{\frac{1}{3} + 1}$

Step 3.2

Write $1$ as a fraction with a common denominator.

$z^{\frac{1}{3} + \frac{3}{3}}$

Step 3.3

Combine the numerators over the common denominator.

$z^{\frac{1 + 3}{3}}$

Step 3.4

Add $1$ and $3$ .

$z^{\frac{4}{3}}$