Question

guided practice
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evaluate the following expression. round the solution to the nearest tenth if necessary.
e^{-2} =
exponential functions

Explanation:

Step1: Recall the property of exponents

We know that \( a^{-n}=\frac{1}{a^{n}} \), so \( e^{-2}=\frac{1}{e^{2}} \).

Step2: Calculate the value of \( e^{2} \)

The value of \( e\approx2.71828 \), so \( e^{2}\approx(2.71828)^{2}\approx7.38906 \).

Step3: Calculate the value of \( \frac{1}{e^{2}} \)

\( \frac{1}{e^{2}}\approx\frac{1}{7.38906}\approx0.135335 \).

Step4: Round to the nearest tenth

Rounding \( 0.135335 \) to the nearest tenth, we look at the hundredth place which is 3. Since \( 3\lt5 \), we round down. So the result is \( 0.1 \).

Answer:

0.1