Finite Math Examples

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

Step 1

Move $y^{- \frac{1}{5}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

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

$y^{\frac{1}{3} + \frac{1}{5}}$

Step 2.2

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

$y^{\frac{1}{3} \cdot \frac{5}{5} + \frac{1}{5}}$

Step 2.3

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

$y^{\frac{1}{3} \cdot \frac{5}{5} + \frac{1}{5} \cdot \frac{3}{3}}$

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

$y^{\frac{5}{3 \cdot 5} + \frac{1}{5} \cdot \frac{3}{3}}$

Step 2.4.2

Multiply $3$ by $5$ .

$y^{\frac{5}{15} + \frac{1}{5} \cdot \frac{3}{3}}$

Step 2.4.3

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

$y^{\frac{5}{15} + \frac{3}{5 \cdot 3}}$

Step 2.4.4

Multiply $5$ by $3$ .

$y^{\frac{5}{15} + \frac{3}{15}}$

Step 2.5

Combine the numerators over the common denominator.

$y^{\frac{5 + 3}{15}}$

Step 2.6

Add $5$ and $3$ .

$y^{\frac{8}{15}}$