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I'd like to get an opinion on how this expression should be interpreted in order to resolve a disagreement. The expression is originally written as: $-\frac{1}{4}cos(2t)^4$

Should this be interpreted as:

(A) $-\frac{1}{4}(cos(2t))^4$ with the cosine evaluated first.

(B) $-\frac{1}{4}cos((2t)^4)$ with the exponent evaluated first.

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    Without more context, both interpretations are valid. The probability of the intent $\cos^4(2t)$ is higher. – 2017-01-09

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I would say it is the cosine first, given that the usage of $()$ clearly suggests that the argument to the function is just $2t$.

If that is so, one would probably better write $-\frac14\cos^4(2t)$ to avoid all misunderstandings.

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    Thanks for sharing your thoughts. I agree and thought that it was cosine first, the intent was the later (B) with the exponent evaluated first. – 2017-01-10
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    @user98724 Then you have proof that not parenthesizing expressions can be tragic – 2017-01-10