Simplify (y^(1/4))/(y^(1/8))

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

Step 1

Move $y^{\frac{1}{8}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 2

Multiply $y^{\frac{1}{4}}$ by $y^{- \frac{1}{8}}$ by adding the exponents.

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

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

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

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

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

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

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

Multiply $4$ by $2$ .

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $2$ .

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