Simplify (y^(5/6)*y^(2/3))/(y^(1/2))

$\frac{y^{\frac{5}{6}} \cdot y^{\frac{2}{3}}}{y^{\frac{1}{2}}}$

Multiply $y^{\frac{5}{6}}$ by $y^{\frac{2}{3}}$ by adding the exponents.

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

$\frac{y^{\frac{5}{6} + \frac{2}{3}}}{y^{\frac{1}{2}}}$

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{y^{\frac{5}{6} + \frac{2}{3} \cdot \frac{2}{2}}}{y^{\frac{1}{2}}}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

$\frac{y^{\frac{5}{6} + \frac{2 \cdot 2}{3 \cdot 2}}}{y^{\frac{1}{2}}}$

Multiply $3$ by $2$ .

$\frac{y^{\frac{5}{6} + \frac{2 \cdot 2}{6}}}{y^{\frac{1}{2}}}$

Combine the numerators over the common denominator.

$\frac{y^{\frac{5 + 2 \cdot 2}{6}}}{y^{\frac{1}{2}}}$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{y^{\frac{5 + 4}{6}}}{y^{\frac{1}{2}}}$

Add $5$ and $4$ .

$\frac{y^{\frac{9}{6}}}{y^{\frac{1}{2}}}$

Cancel the common factor of $9$ and $6$ .

Factor $3$ out of $9$ .

$\frac{y^{\frac{3 (3)}{6}}}{y^{\frac{1}{2}}}$

Cancel the common factors.

Factor $3$ out of $6$ .

$\frac{y^{\frac{3 \cdot 3}{3 \cdot 2}}}{y^{\frac{1}{2}}}$

Cancel the common factor.

$\frac{y^{\frac{3 \cdot 3}{3 \cdot 2}}}{y^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{y^{\frac{3}{2}}}{y^{\frac{1}{2}}}$

Move $y^{\frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$y^{\frac{3}{2}} y^{- \frac{1}{2}}$

Multiply $y^{\frac{3}{2}}$ by $y^{- \frac{1}{2}}$ by adding the exponents.

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

$y^{\frac{3}{2} - \frac{1}{2}}$

Combine the numerators over the common denominator.

$y^{\frac{3 - 1}{2}}$

Subtract $1$ from $3$ .

$y^{\frac{2}{2}}$

Divide $2$ by $2$ .

$y^{1}$

Simplify $y^{1}$ .

$y$