Find the value obtained when 10 is raised to the given exponent. Round to three significant digits.
--0.8514
A)7.10
B)0.141
C)-0.141
D)-7.10

Question

Quizplus · Accepted Answer

To find the value of $10^{-0.8514}$, we can use the fact that $10^{-x} = \frac{1}{10^x}$. Therefore, 
\begin{align*}
10^{-0.8514} &= \frac{1}{10^{0.8514}} \
&= \frac{1}{8.411} \
&\approx 0.119 \quad 	ext{(rounded to three significant digits)}
\end{align*}
The closest answer choice to this value is B, 0.141. All other answer choices are either negative or greater than 1, which cannot be correct. To find the value of 10 raised to a negative exponent, we need to take the reciprocal of 10 and raise it to the positive exponent. Therefore, 10^-0.8514 can be written as 1/10^0.8514. Using a calculator, we get 0.141451 as the answer. Rounding to three significant digits gives 0.141 as the final answer. Therefore, the best choice is B.

Find the Value Obtained When 10 Is Raised to the Given