Convert to Radical Form (y^(1/9))/(y^(1/18))

$\frac{y^{\frac{1}{9}}}{y^{\frac{1}{18}}}$

Step 1

Move $y^{\frac{1}{18}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$y^{\frac{1}{9}} y^{- \frac{1}{18}}$

Step 2

Multiply $y^{\frac{1}{9}}$ by $y^{- \frac{1}{18}}$ by adding the exponents.

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

$y^{\frac{1}{9} - \frac{1}{18}}$

To write $\frac{1}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y^{\frac{1}{9} \cdot \frac{2}{2} - \frac{1}{18}}$

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{9}$ by $\frac{2}{2}$ .

$y^{\frac{2}{9 \cdot 2} - \frac{1}{18}}$

Multiply $9$ by $2$ .

$y^{\frac{2}{18} - \frac{1}{18}}$

Combine the numerators over the common denominator.

$y^{\frac{2 - 1}{18}}$

Subtract $1$ from $2$ .

$y^{\frac{1}{18}}$

Step 3

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt[18]{y^{1}}$

Step 4

Anything raised to $1$ is the base itself.

$\sqrt[18]{y}$