The best replacement for exponent is power.

The best alternatives to exponent are rated as following:
★★★★★  power
★  logarithm

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Speaking about exponent, one probably shouldn't forget about negative number.

Other search terms related to exponent and their ratings are:
★★★★★ negative number
★★★★ fractions
★★★★ 0
★★★★ an exponent
★★★ negative base
★★★ negative
★★★ decimal
★★ zero
★ square root
★ different bases
★ fraction base
★ fraction
variable
log
negative fraction
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Google Trends

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exponent
power
logarithm