Basic Math Examples

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

Step 1

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

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

Step 1.2

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

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

Step 1.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{3}{2}$ by $\frac{2}{2}$ .

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

Step 1.3.2

Multiply $2$ by $2$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $3$ by $2$ .

$\frac{z^{\frac{6 - 1}{4}}}{z^{\frac{1}{3}}}$

Step 1.5.2

Subtract $1$ from $6$ .

$\frac{z^{\frac{5}{4}}}{z^{\frac{1}{3}}}$

Step 2

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

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

Step 3

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

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

Step 3.2

To write $\frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3.3

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 3.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{5}{4}$ by $\frac{3}{3}$ .

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

Step 3.4.2

Multiply $4$ by $3$ .

$z^{\frac{5 \cdot 3}{12} - \frac{1}{3} \cdot \frac{4}{4}}$

Step 3.4.3

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$z^{\frac{5 \cdot 3}{12} - \frac{4}{3 \cdot 4}}$

Step 3.4.4

Multiply $3$ by $4$ .

$z^{\frac{5 \cdot 3}{12} - \frac{4}{12}}$

Step 3.5

Combine the numerators over the common denominator.

$z^{\frac{5 \cdot 3 - 4}{12}}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $5$ by $3$ .

$z^{\frac{15 - 4}{12}}$

Step 3.6.2

Subtract $4$ from $15$ .

$z^{\frac{11}{12}}$