Simplify the following expression using exponents: $$ \frac{y^{\frac{5}{6}}}{y^{\frac{1}{3}}} $$

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UpStudy AI · Accepted Answer

To simplify the expression $$ \frac{y^{\frac{5}{6}}}{y^{\frac{1}{3}}} $$, you can use the properties of exponents, specifically the quotient rule which states:

$$
\frac{y^a}{y^b} = y^{a - b}
$$

Applying this rule:

$$
\frac{y^{\frac{5}{6}}}{y^{\frac{1}{3}}} = y^{\frac{5}{6} - \frac{1}{3}}
$$

First, find a common denominator to subtract the exponents:

$$
\frac{5}{6} - \frac{1}{3} = \frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2}
$$

So, the simplified expression is:

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

Alternatively, $$ y^{\frac{1}{2}} $$ can be written as the square root of $$ y $$:

$$
\sqrt{y}
$$

**Final Answer:**

$$
y^{\,\frac{1}{2}}
$$
The simplified expression is $$ y^{\frac{1}{2}} $$ or $$ \sqrt{y} $$.

Simplify the following expression using exponents: \( \frac{y^{\frac{5}{6}}}{y^{\frac{1}{3}}} \)

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