SOLUTION: Evaluate 4 to the 5/2

Question 1209253: Evaluate 4 to the 5/2
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

Unclear.

To me, it is unclear what you want.

The wording in your post is ambiguous.

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In addition to interpretation by the other tutor, it can be interpreted as .

Using words instead of formulas in Math almost always leads to ambiguity.

It is why special mathematical language was developed 200 - 300 years ago
to use it in Math, which never produces ambiguity.

Using right accurate language in Math is a form of respectful communication in Math.
                             It is MUST.

Using wrong inaccurate language in Math of the type " bla-bla-bla " is a form
of disrespectful communication in Math.

                             Learn and memorize.

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Your question could be interpreted as either 4^(5/2) or (4^5)/2
The 1st case has "5/2" as the exponent.
The 2nd case is all of "4^5" over top 2.

If we go with the 1st option, then,
4^(5/2)
= ( 4^(1/2) )^5
= ( sqrt(4) )^5
= ( 2 )^5
= 32

Or, if it's the 2nd option,
(4^5)/2
= (1024)/2
= 512

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