1. The problem asks to express each expression in terms of $y=3^x$ and simplify. 2. Recall the properties of exponents: - $a^{m+n} = a^m \cdot a^n$ - $a^{m-n} = \frac{a^m}{a^n}$ - $(a^m)^n = a^{mn}$ 3. For part (b), the expression is $\frac{1}{3^{x-2}}$. 4. Rewrite the denominator using exponent rules: $$3^{x-2} = 3^x \cdot 3^{-2} = 3^x \cdot \frac{1}{3^2} = \frac{3^x}{9}$$ 5. Substitute back: $$\frac{1}{3^{x-2}} = \frac{1}{\frac{3^x}{9}} = \frac{9}{3^x}$$ 6. Since $y = 3^x$, replace $3^x$ with $y$: $$\frac{9}{y}$$ 7. Therefore, the simplified expression is $\frac{9}{y}$, not $y^{-3}$. 8. Note that $y^{-3} = (3^x)^{-3} = 3^{-3x}$, which is different from $\frac{9}{y} = 9 \cdot 3^{-x}$. 9. The key is carefully applying exponent rules and rewriting expressions step-by-step.