1. The problem is to simplify the expression $\left(\frac{3}{4}\right)^{-2}$ and express the answer with positive exponents. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$, where $a \neq 0$ and $n$ is a positive integer. 3. Apply the negative exponent rule: $$\left(\frac{3}{4}\right)^{-2} = \frac{1}{\left(\frac{3}{4}\right)^2}$$ 4. Calculate the square of the fraction: $$\left(\frac{3}{4}\right)^2 = \frac{3^2}{4^2} = \frac{9}{16}$$ 5. Substitute back: $$\frac{1}{\frac{9}{16}}$$ 6. Simplify the complex fraction by multiplying numerator and denominator: $$= 1 \times \frac{16}{9} = \frac{16}{9}$$ 7. The expression with positive exponents is: $$\boxed{\frac{16}{9}}$$ This is the simplified form with positive exponents.