Simplify (y^(1/6))/(y^(1/12))

$\frac{y^{\frac{1}{6}}}{y^{\frac{1}{12}}}$

Step 1

Move $y^{\frac{1}{12}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$y^{\frac{1}{6}} y^{- \frac{1}{12}}$

Step 2

Multiply $y^{\frac{1}{6}}$ by $y^{- \frac{1}{12}}$ by adding the exponents.

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

$y^{\frac{1}{6} - \frac{1}{12}}$

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y^{\frac{1}{6} \cdot \frac{2}{2} - \frac{1}{12}}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{6}$ by $\frac{2}{2}$ .

$y^{\frac{2}{6 \cdot 2} - \frac{1}{12}}$

Multiply $6$ by $2$ .

$y^{\frac{2}{12} - \frac{1}{12}}$

Combine the numerators over the common denominator.

$y^{\frac{2 - 1}{12}}$

Subtract $1$ from $2$ .

$y^{\frac{1}{12}}$