Basic Math Examples

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

Step 1

Multiply $z^{\frac{5}{4}}$ 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.

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

Step 1.2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 1.3

Combine $- 2$ and $\frac{4}{4}$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 2$ by $4$ .

$\frac{z^{\frac{3}{4}}}{z^{\frac{5 - 8}{4}}}$

Step 1.5.2

Subtract $8$ from $5$ .

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

Step 1.6

Move the negative in front of the fraction.

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

Step 2

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

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

Step 3

Multiply $z^{\frac{3}{4}}$ by $z^{\frac{3}{4}}$ by adding the exponents.

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Step 3.1

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

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

Add $3$ and $3$ .

$z^{\frac{6}{4}}$

Step 3.4

Cancel the common factor of $6$ and $4$ .

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Step 3.4.1

Factor $2$ out of $6$ .

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

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $2$ out of $4$ .

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

Step 3.4.2.2

Cancel the common factor.

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

Step 3.4.2.3

Rewrite the expression.

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