The problem asks us to simplify the expression $x^{-1}/7 + 4^2/9$ and write it as a single fraction with positive exponents.

1. Problem Description

The problem asks us to simplify the expression $x^{-1}/7 + 4^2/9$ and write it as a single fraction with positive exponents.

2. Solution Steps

First, we rewrite the expression with positive exponents. Recall that $a^{-n} = \frac{1}{a^n}$.

So, $x^{-1} = \frac{1}{x^1} = \frac{1}{x}$.

Also, $4^2 = 16$.

The expression becomes:

$\frac{1}{7x} + \frac{16}{9}$

Now, we find a common denominator to combine the fractions. The common denominator is $63x$.

$\frac{1}{7x} + \frac{16}{9} = \frac{1}{7x} \cdot \frac{9}{9} + \frac{16}{9} \cdot \frac{7x}{7x} = \frac{9}{63x} + \frac{112x}{63x}$

Combining the fractions gives:

$\frac{9 + 112x}{63x}$

3. Final Answer

The simplified expression is $\frac{112x+9}{63x}$.