Rational Exponents

General Mathematics — Second Secondary

Definition of rational exponents

Comparison aspect	Main idea	Keywords
a1/n = ⁿ√a	so the exponent 1/n means the n-th root	exponentmeansroot
am/n = (ⁿ√a)m = ⁿ√(am)	so the numerator is the power and the denominator is the root	numeratorpowerdenominatorroot
a−m/n = 1 / am/n	so a negative exponent means the reciprocal of the power	negativeexponentmeansreciprocal
•	It is usually easier to take the root first and then raise the result to the power because the numbers stay small	usuallyeasiertakeroot
For example	251/2 = √25 = 5 and 253/2 = (√25)3 = 53 = 125. Notice that the exponent 3/2 means taking the square root and then raising to the power 3	Noticeexponentmeanstaking

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