A fractional index of a half is the equivalent of finding a square root.
Using the rules for multiplying powers, notice that:
9½ x 9½ = 91
Which is then the equivalent of:
√9 x √9 = 9
9½ = √9 = 3
Understanding this explanation is helpful, but the important thing is to remember that any number to the power of a half, simply means the square root of that number.
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