Name___________________________________ Date_______________ Period_________ RADICALS AND RATIONAL EXPONENTS WORKSHEET #2 REVIEW: nth Root: If b a , then b is the n n th root of a. This is written n a b . n is called the index of the radical. a is 1 m th called the radicand. Roots as Rational Exponents: The n root, n a , can be written as an exponent a n . a n a n Notice the placement of the m and n. The root index is the denominator and the exponent is the numerator. Simplify. 1) 121x 4 2) 81 144 3) 3 27a12 4) If f ( x) 4 x 1 , a) Find f(-2) b) Find the domain of f(x) Evaluate. 5) (27) 1 6) ( 16) 3 1 4 7) 16 3 4 Write in exponential form. 8) 5 9) ( 6 a ) 5 a2 Write as a radical expression with a smaller index. 10) 4 49 4 x 11) 14 x7 Simplify. 3 12) x 13) x2 4 x 14) 3 2 5 Use laws of exponents, reduce fractions, and write answers in simplified radical form. 4 13) 5 x3 x3 14) 5 4 x x 1 4 15) x x 3 1 2 m - Use laws of exponents, reduce fractions, and write answers in simplified radical form. 7 16) 4 y 8 98 3 y 56 19) 2 y 22) 10 53 17) y 4 20) z 1 18) 3y 3 1 2 21) z 4 3 9 2 5 a7 16a 4 a3 a 23) 4 7 6a 2 1 a2 1 1 25) x 3 x 4 24) 3 4 3 26) x 5 x 1 3 Simplify. 27) 10 30) 4 33) 25 28) 16x8 31) 9 27x 6 9 8 a3 29) 14 81 32) 6 y7 25x 4