da6965…: “Against an amazing angle”

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1 : Compute the following numeric exponential value.

$\sage {p1b1}^{\sage {p1pwr1}} = \answer {\sage {p1ans1}}$
$\left (\frac {1}{\sage {p1b1}}\right )^{\sage {p1pwr1}} = \answer {\sage {p1ans2}}$
$\left (\sage {p1b1}\right )^{-\sage {p1pwr1}} = \answer {\sage {p1ans2}}$
$\left (\frac {1}{\sage {p1b1}}\right )^{-\sage {p1pwr1}} = \answer {\sage {p1ans1}}$

Remember that you can distribute a power over the top and bottom of a fraction, and that negative powers “flip” a fraction. So for example, $\left (\frac {1}{2}\right )^{-5} = \left (\frac {2}{1}\right )^{5} = \frac {2^5}{1^5} = \frac {32}{1} = 32.$

2 : Compute the following numeric exponential value.

$\sage {p2b1}^{\sage {p2pwr1}} = \answer {\sage {p2ans1}}$
$\left (\frac {1}{\sage {p2b1}}\right )^{\sage {p2pwr1}} = \answer {\sage {p2ans2}}$
$\left (\sage {p2b1}\right )^{-\sage {p2pwr1}} = \answer {\sage {p2ans2}}$
$\left (\frac {1}{\sage {p2b1}}\right )^{-\sage {p2pwr1}} = \answer {\sage {p2ans1}}$

3 : Compute the following numeric exponential value.

$\sage {p3b1}^{\sage {p3pwr1}} = \answer {\sage {p3ans1}}$
$\left (\frac {1}{\sage {p3b1}}\right )^{\sage {p3pwr1}} = \answer {\sage {p3ans2}}$
$\left (\sage {p3b1}\right )^{-\sage {p3pwr1}} = \answer {\sage {p3ans2}}$
$\left (\frac {1}{\sage {p3b1}}\right )^{-\sage {p3pwr1}} = \answer {\sage {p3ans1}}$

4 : Compute the following numeric exponential value.

$\sage {p4b1}^{\sage {p4pwr1}} = \answer {\sage {p4ans1}}$
$\left (\frac {1}{\sage {p4b1}}\right )^{\sage {p4pwr1}} = \answer {\sage {p4ans2}}$
$\left (\sage {p4b1}\right )^{-\sage {p4pwr1}} = \answer {\sage {p4ans2}}$
$\left (\frac {1}{\sage {p4b1}}\right )^{-\sage {p4pwr1}} = \answer {\sage {p4ans1}}$