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How do you work out negative fractional indices?

Updated: 12/9/2022
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GeorginaRogers

Lvl 1
10y ago

Best Answer

A number with a negative index is simply the reciprocal of the same number with a positive index.

So, x-a = 1/xa

Next a number to a fractional index, (a/b) is the ath power of the bth root of the number. Equivalently, it is the bth root of the ath power of the number.

That is, xa/b = b√(xa) = (b√x)a.

Combining these results: x-a/b = 1/(xa/b) = 1/[b√(xa)]

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Q: How do you work out negative fractional indices?
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