Algebra II Review 6.1 and 6.2 KEY

Algebra II Review 6.1-6.2 ANSWER KEY6.1 Evaluate Nth Roots and use Rational ExponentsThings you should be able to do:- Rewrite radical expressions using rational exponent notation- Rewrite rational exponent expressions using radical notation- Evaluate an Nth root without using a calculator- Solve an equation using Nth rootsExamples:Rewrite the radical expression using rational exponent notation:1.2 2= 2. (3 1 3 2 391 96 ) = ( 6 ) = 63. ( − 2 ) = (( − 2) ) = ( − 2)37 7 1 34 4 4 9Rewrite the rational exponent expression using radical notation.13 34. 17 173337= 5. 4 ( 4 ) ( )1 7 71 575= = 46. ( − 28 ) 5 = (( − 28) ) = ( − 28)Evaluate the expression using Nth roots without using a calculator.237 77. (3 28) = ( 2)= 4 8. (4 381) = ( 3)= 279.2( ) ( )3336 = 36 = 6 = 216343 310. ( ) ( )125 125 5 62544− 8 = − 8 = − 2= = = 11. ( ) 1 335 5 551 312. ( ) 33( ) ( ) ( )− 27 = ( − 27) = − 27 = − 3 = − 243Solve an equation using Nth roots. (Round decimals to two places)52x+ 73 = 53( x + 3) 4 = 3623x + 17 = 132542x= −20x + 3 = ± 3623x = 1155413.14. x = −1015. x = ± 362 − 33x = 1155x = −10x ≈ 1.36x ≈ 4.86x ≈ −1.58x ≈ −7.36

Simplify the following radical expressions. Leave your answer in radical form.10.84 7 9 3 4 4 3 3 2 4 3 33x y z = 3x x y yz = xy 3x yz 11.x y z = x y yz z = xyz yz3 3 4 7 3 3 3 6 2 312.x y z = ⋅ x xy z z = x y z xz 13. 5 3a b c = 5 3a b b c c = a b c 5 3b c5 8 3 4 8 2 2 424 4 6 2 610 17 29 10 15 2 25 4 2 3 5 2 4