4 ^ (1/7 ) is the 7th root of 4 or the 3rd box
4 ^ (7/2) is 4 to the 7th power then the square root or the 2nd box
7 ^ (1/4) is the 4th root of 7 or the 4th box
7 ^ (1/2) is the square root of 7 or the 6th box
Step-by-step explanation:
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Recall the Maclaurin expansion for cos(x), valid for all real x :

Then replacing x with √5 x (I'm assuming you mean √5 times x, and not √(5x)) gives

The first 3 terms of the series are

and the general n-th term is as shown in the series.
In case you did mean cos(√(5x)), we would instead end up with

which amounts to replacing the x with √x in the expansion of cos(√5 x) :

<span> -9x4 + 5x2 - 26x - 12
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