Subjects algebra

Exponent Evaluation Fa4997

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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: $\left(\frac{3}{5}\right)^{-0.85} = 2.252$ $3.5^{1.6} = 7.254$