Exponentiation 53Unit 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 //^4d. ⎛⎝⎜⎛⎛⎝⎝− ⎞⎠⎟⎞⎞⎠⎠32
24315 /Solutiona. ()^13 //Step 1. Apply xx1/n n.()−^13 / =−^327Step 2. Find the principal cube root of −27.()−^13 / =−^327 =− 3b. () 02512 /
Step 1. Apply xx^1 /n n.() 02. 25512 00. 25Step 2. Find the principal square root of 0.25.() 02. 25512 000. 2525 = 05.c. ()^1 //^4
Step 1. Apply xx1/n n.()−^14 / =−^416P