Finite Math Examples

$y^{\frac{1}{2}} \cdot y^{\frac{1}{8}}$

Step 1

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

$y^{\frac{1}{2} + \frac{1}{8}}$

Step 2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y^{\frac{1}{2} \cdot \frac{4}{4} + \frac{1}{8}}$

Step 3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{2}$ by $\frac{4}{4}$ .

$y^{\frac{4}{2 \cdot 4} + \frac{1}{8}}$

Step 3.2

Multiply $2$ by $4$ .

$y^{\frac{4}{8} + \frac{1}{8}}$

Step 4

Combine the numerators over the common denominator.

$y^{\frac{4 + 1}{8}}$

Step 5

Add $4$ and $1$ .

$y^{\frac{5}{8}}$