Simplify (x^(5/6))/(x^(1/6))

$\frac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}$

Move $x^{\frac{1}{6}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$x^{\frac{5}{6}} x^{- \frac{1}{6}}$

Multiply $x^{\frac{5}{6}}$ by $x^{- \frac{1}{6}}$ by adding the exponents.

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

$x^{\frac{5}{6} - \frac{1}{6}}$

Combine the numerators over the common denominator.

$x^{\frac{5 - 1}{6}}$

Subtract $1$ from $5$ .

$x^{\frac{4}{6}}$

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4$ .

$x^{\frac{2 (2)}{6}}$

Cancel the common factors.

Factor $2$ out of $6$ .

$x^{\frac{2 \cdot 2}{2 \cdot 3}}$

Cancel the common factor.

$x^{\frac{2 \cdot 2}{2 \cdot 3}}$

Rewrite the expression.

$x^{\frac{2}{3}}$