1. The problem asks to evaluate the expressions $\left(\frac{3}{5}\right)^{-0.85}$ and $3.5^{1.6}$ and round the answers to the nearest thousandth.
2. Recall the rule for negative exponents: $a^{-b} = \frac{1}{a^b}$. Also, for any positive base $a$ and exponent $b$, $a^b$ means $a$ raised to the power $b$.
3. Evaluate $\left(\frac{3}{5}\right)^{-0.85}$:
$$\left(\frac{3}{5}\right)^{-0.85} = \frac{1}{\left(\frac{3}{5}\right)^{0.85}}$$
Calculate $\left(\frac{3}{5}\right)^{0.85}$ first (do not round intermediate steps).
4. Using a calculator, $\left(\frac{3}{5}\right)^{0.85} \approx 0.444$ (exact intermediate value kept internally).
5. Then,
$$\left(\frac{3}{5}\right)^{-0.85} = \frac{1}{0.444} \approx 2.252$$
Rounded to the nearest thousandth, the answer is $2.252$.
6. Next, evaluate $3.5^{1.6}$:
Using a calculator, $3.5^{1.6} \approx 7.254$.
Rounded to the nearest thousandth, the answer is $7.254$.
Final answers:
$\left(\frac{3}{5}\right)^{-0.85} = 2.252$
$3.5^{1.6} = 7.254$
Exponent Evaluation Fa4997
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.