Finite Math Examples

$\frac{z^{\frac{5}{2} Z} - \frac{1}{2}}{z^{\frac{1}{3}}}$

Step 1

Simplify the numerator.

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Step 1.1

Combine $\frac{5}{2}$ and $Z$ .

$\frac{z^{\frac{5 Z}{2}} - \frac{1}{2}}{z^{\frac{1}{3}}}$

Step 1.2

To write $z^{\frac{5 Z}{2}}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{z^{\frac{5 Z}{2}} \cdot \frac{2}{2} - \frac{1}{2}}{z^{\frac{1}{3}}}$

Step 1.3

Combine $z^{\frac{5 Z}{2}}$ and $\frac{2}{2}$ .

$\frac{\frac{z^{\frac{5 Z}{2}} \cdot 2}{2} - \frac{1}{2}}{z^{\frac{1}{3}}}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{\frac{z^{\frac{5 Z}{2}} \cdot 2 - 1}{2}}{z^{\frac{1}{3}}}$

Step 1.5

Move $2$ to the left of $z^{\frac{5 Z}{2}}$ .

$\frac{\frac{2 z^{\frac{5 Z}{2}} - 1}{2}}{z^{\frac{1}{3}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{2 z^{\frac{5 Z}{2}} - 1}{2} \cdot \frac{1}{z^{\frac{1}{3}}}$

Step 3

Multiply $\frac{2 z^{\frac{5 Z}{2}} - 1}{2}$ by $\frac{1}{z^{\frac{1}{3}}}$ .

$\frac{2 z^{\frac{5 Z}{2}} - 1}{2 z^{\frac{1}{3}}}$