We are asked to simplify the expression $\frac{a^{\frac{7}{12}}}{a^{\frac{1}{3}}}$. We need to express the answer with positive exponents.

1. Problem Description

We are asked to simplify the expression $\frac{a^{\frac{7}{12}}}{a^{\frac{1}{3}}}$. We need to express the answer with positive exponents.

2. Solution Steps

We will use the property of exponents:

$\frac{a^m}{a^n} = a^{m-n}$

In our case, $m = \frac{7}{12}$ and $n = \frac{1}{3}$. Therefore, we have

$\frac{a^{\frac{7}{12}}}{a^{\frac{1}{3}}} = a^{\frac{7}{12} - \frac{1}{3}}$

To subtract the fractions, we need a common denominator. The common denominator of 12 and 3 is

1

2. We can rewrite $\frac{1}{3}$ as $\frac{4}{12}$.

So, we have

$\frac{7}{12} - \frac{1}{3} = \frac{7}{12} - \frac{4}{12} = \frac{7-4}{12} = \frac{3}{12} = \frac{1}{4}$.

Therefore,

$a^{\frac{7}{12} - \frac{1}{3}} = a^{\frac{1}{4}}$.

3. Final Answer

$a^{\frac{1}{4}}$