Solve {left(cos(pi/12)+sin(pi/12)right)}^22

$${ \left( \cos ( \frac{ \pi }{ 12 } ) + \sin ( \frac{ \pi }{ 12 } ) \right) }^{ 22 }$$

Evaluate

$$86.49755859374998586299277104467747205844693855647036789939179227617232684109009971084289037503528879041598950032694540931557484525586991759144454386680837015903297585053357815136105085035939434825998420900418719003483764209483372939136422504028873964641853911294565682783331182984375381492302658948484629866637657195098557535069679978808885733740765365659081652675501533167616$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(0.9659258262890683 + 0.25881904510252074)} ^ {22}$$

Add 0.9659258262890683 and 0.25881904510252074 to get 1.22474487139158904.

$$1.22474487139158904^{22}$$

Calculate 1.22474487139158904 to the power of 22 and get 86.49755859374998586299277104467747205844693855647036789939179227617232684109009971084289037503528879041598950032694540931557484525586991759144454386680837015903297585053357815136105085035939434825998420900418719003483764209483372939136422504028873964641853911294565682783331182984375381492302658948484629866637657195098557535069679978808885733740765365659081652675501533167616.

$$86.49755859374998586299277104467747205844693855647036789939179227617232684109009971084289037503528879041598950032694540931557484525586991759144454386680837015903297585053357815136105085035939434825998420900418719003483764209483372939136422504028873964641853911294565682783331182984375381492302658948484629866637657195098557535069679978808885733740765365659081652675501533167616$$

Factor

$$\frac{17 ^ {22} \cdot 29 ^ {22} \cdot 137 ^ {22} \cdot 509 ^ {22} \cdot 445318127 ^ {22}}{2 ^ {308} \cdot 5 ^ {374}} = NaN$$