Questions: Use a calculator to find the following power. 2 π^(-3) 2 π^(-3)= (Round to eight decimal places as needed.)

Solution Steps

To solve the given problem, we need to calculate \(2 \pi^{-3}\). This involves raising \(\pi\) to the power of -3 and then multiplying the result by 2. Finally, we will round the result to eight decimal places.

We start by calculating \( \pi^{-3} \): \[ \pi^{-3} = \frac{1}{\pi^3} \]

Next, we multiply the result by 2: \[ 2 \pi^{-3} = 2 \cdot \frac{1}{\pi^3} = \frac{2}{\pi^3} \]

Using the approximate value of \( \pi \approx 3.14159265 \), we compute: \[ \pi^3 \approx 31.00627668 \] Thus, \[ 2 \pi^{-3} \approx \frac{2}{31.00627668} \approx 0.06450306886639899 \] Rounding this to eight decimal places gives: \[ 0.06450307 \]

Final Answer