Exponentiation 53
Unit Fraction and Rational Exponents
Unit Fraction Exponents
If x is a real number and n is a natural number, then xx1/n n , provided
that, when n is even, x≥ 0.
A unit fraction exponent on a number tells you to fi nd the principal nth
root of the number.
Problem Evaluate, if possible.
a. ()^13 //
b. (.. 25 )^12 //
c. ()^1 //^4
d. ⎛⎝⎜⎛⎛⎝⎝− ⎞⎠⎟⎞⎞⎠⎠
32
243
15 /
Solution
a. ()^13 //
Step 1. Apply xx1/n n.
()−^13 / =−^327
Step 2. Find the principal cube root of −27.
()−^13 / =−^327 =− 3
b. () 02512 /
Step 1. Apply xx^1 /n n.
() 02. 25512 00. 25
Step 2. Find the principal square root of 0.25.
() 02. 25512 000. 2525 = 05.
c. ()^1 //^4
Step 1. Apply xx1/n n.
()−^14 / =−^416
P