Basic Math Examples

$\frac{z^{\frac{3}{4}}}{z^{\frac{5}{4} \cdot z^{- 2}}}$

Step 1

Factor $z^{\frac{5}{4} z^{- 2}}$ out of $z^{\frac{3}{4}}$ .

$\frac{z^{\frac{5}{4} z^{- 2}} z^{\frac{3 - 1 z^{- 2} \frac{5}{4} \cdot 4}{4}}}{z^{\frac{5}{4} z^{- 2}}}$

Step 2

Cancel the common factors.

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Step 2.1

Multiply by $1$ .

$\frac{z^{\frac{5}{4} z^{- 2}} z^{\frac{3 - 1 z^{- 2} \frac{5}{4} \cdot 4}{4}}}{z^{\frac{5}{4} z^{- 2}} \cdot 1}$

Step 2.2

Cancel the common factor.

$\frac{z^{\frac{5}{4} z^{- 2}} z^{\frac{3 - 1 z^{- 2} \frac{5}{4} \cdot 4}{4}}}{z^{\frac{5}{4} z^{- 2}} \cdot 1}$

Step 2.3

Rewrite the expression.

$\frac{z^{\frac{3 - 1 z^{- 2} \frac{5}{4} \cdot 4}{4}}}{1}$

Step 2.4

Divide $z^{\frac{3 - 1 z^{- 2} \frac{5}{4} \cdot 4}{4}}$ by $1$ .

$z^{\frac{3 - 1 z^{- 2} \frac{5}{4} \cdot 4}{4}}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$z^{\frac{3 - 1 \frac{1}{z^{2}} \frac{5}{4} \cdot 4}{4}}$

Step 3.2

Rewrite $- 1 \frac{1}{z^{2}}$ as $- \frac{1}{z^{2}}$ .

$z^{\frac{3 - \frac{1}{z^{2}} \cdot \frac{5}{4} \cdot 4}{4}}$

Step 3.3

Multiply $\frac{5}{4}$ by $\frac{1}{z^{2}}$ .

$z^{\frac{3 - \frac{5}{4 z^{2}} \cdot 4}{4}}$

Step 3.4

Cancel the common factor of $4$ .

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Step 3.4.1

Move the leading negative in $- \frac{5}{4 z^{2}}$ into the numerator.

$z^{\frac{3 + \frac{- 5}{4 z^{2}} \cdot 4}{4}}$

Step 3.4.2

Factor $4$ out of $4 z^{2}$ .

$z^{\frac{3 + \frac{- 5}{4 (z^{2})} \cdot 4}{4}}$

Step 3.4.3

Cancel the common factor.

$z^{\frac{3 + \frac{- 5}{4 z^{2}} \cdot 4}{4}}$

Step 3.4.4

Rewrite the expression.

$z^{\frac{3 + \frac{- 5}{z^{2}}}{4}}$

Step 3.5

Move the negative in front of the fraction.

$z^{\frac{3 - \frac{5}{z^{2}}}{4}}$

Step 3.6

To write $3$ as a fraction with a common denominator, multiply by $\frac{z^{2}}{z^{2}}$ .

$z^{\frac{\frac{3 z^{2}}{z^{2}} - \frac{5}{z^{2}}}{4}}$

Step 3.7

Combine the numerators over the common denominator.

$z^{\frac{\frac{3 z^{2} - 5}{z^{2}}}{4}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$z^{\frac{3 z^{2} - 5}{z^{2}} \cdot \frac{1}{4}}$

Step 5

Multiply $\frac{3 z^{2} - 5}{z^{2}}$ by $\frac{1}{4}$ .

$z^{\frac{3 z^{2} - 5}{z^{2} \cdot 4}}$

Step 6

Move $4$ to the left of $z^{2}$ .

$z^{\frac{3 z^{2} - 5}{4 z^{2}}}$