Query about Question 2 from "PrepSwift: Common Exponent Mistakes" [3423]

[user8970]

https://prepswift.gregmat.com/quizzes/quiz/prepswift-common-exponent-mistakes (Question 2)

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Hi,
if I have 2 to the power of (7/2), how come it doesn’t translate to square root of (2 to the power of 7)? Is it the parenthesis in the first term?
I did go through the “old” roots as exponents II but that didn’t answer my question
Thank you!

[cylverixxx]

@user8970

how come it doesn’t translate to square root of (2 to the power of 7)? Is it the parenthesis in the first term?

It does.

2^{\frac 72} = \left (2^7 \right)^{\frac 12} = \sqrt{2^7}