Simplify (y^(1/8))/(y^(1/16))

$\frac{y^{\frac{1}{8}}}{y^{\frac{1}{16}}}$

Move $y^{\frac{1}{16}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$y^{\frac{1}{8}} y^{- \frac{1}{16}}$

Multiply $y^{\frac{1}{8}}$ by $y^{- \frac{1}{16}}$ by adding the exponents.

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

$y^{\frac{1}{8} - \frac{1}{16}}$

To write $\frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y^{\frac{1}{8} \cdot \frac{2}{2} - \frac{1}{16}}$

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{8}$ by $\frac{2}{2}$ .

$y^{\frac{2}{8 \cdot 2} - \frac{1}{16}}$

Multiply $8$ by $2$ .

$y^{\frac{2}{16} - \frac{1}{16}}$

Combine the numerators over the common denominator.

$y^{\frac{2 - 1}{16}}$

Subtract $1$ from $2$ .

$y^{\frac{1}{16}}$