Basic Math Examples

$\frac{v^{\frac{1}{3}}}{v^{\frac{3}{5}}}$

Step 1

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

$\frac{1}{v^{\frac{3}{5}} v^{- \frac{1}{3}}}$

Step 2

Multiply $v^{\frac{3}{5}}$ by $v^{- \frac{1}{3}}$ by adding the exponents.

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Step 2.1

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

$\frac{1}{v^{\frac{3}{5} - \frac{1}{3}}}$

Step 2.2

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

$\frac{1}{v^{\frac{3}{5} \cdot \frac{3}{3} - \frac{1}{3}}}$

Step 2.3

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{v^{\frac{3}{5} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{5}{5}}}$

Step 2.4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

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

$\frac{1}{v^{\frac{3 \cdot 3}{5 \cdot 3} - \frac{1}{3} \cdot \frac{5}{5}}}$

Step 2.4.2

Multiply $5$ by $3$ .

$\frac{1}{v^{\frac{3 \cdot 3}{15} - \frac{1}{3} \cdot \frac{5}{5}}}$

Step 2.4.3

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$\frac{1}{v^{\frac{3 \cdot 3}{15} - \frac{5}{3 \cdot 5}}}$

Step 2.4.4

Multiply $3$ by $5$ .

$\frac{1}{v^{\frac{3 \cdot 3}{15} - \frac{5}{15}}}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{1}{v^{\frac{3 \cdot 3 - 5}{15}}}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $3$ by $3$ .

$\frac{1}{v^{\frac{9 - 5}{15}}}$

Step 2.6.2

Subtract $5$ from $9$ .

$\frac{1}{v^{\frac{4}{15}}}$