Evaluate nth Roots, Properties of rational exponents

Evaluate nth Roots,Properties of rational exponents Chapter 6.1 & 6.2

Objectives • Find nth roots • Evaluate and solve expressions with rational exponents

nth Roots • bn=a • b is the nth root of a • Example: • 34=81 Three is the 4th root of 81 • 4√81 = 3 • Remember, • If “a” is positive and “n” is even, there are two real nth roots • +4√16 = + 2 • If “a” is negative and “n” is odd, there is one real nth root 24 = 16; -24 = 16 53 = 125 -53 = -125

Example – Find the nth Root n=5, a=-32 5√-32 b=-2 n=6, a=1 6√1 b=+1 n=3, a=-216 3√-216 b=-6 n=4, a=81 4√81 b=+3

Evaluate Expressions with Rational Exponents am/n = (a1/n)m = (n√a)m 1252/3 (1251/3)2 (3√125)2 = 25 8-4/3 (81/3)-4 (3√8)-4 = 1/16 45/2 (√4)5 = 32 (41/2)5 64-2/3 (3√64)-2 =1/16 (641/3)-2

Now you try  • Page 417 • 3-8, 13-15, 21-23, 34, 50-53, 60 • Homework: p 419 75-82

Apply properties of rational exponents • The properties we learned with whole numbers, still hold true with fractions. • Page 420 in books has an additional table with the properties listed with fractions.

Apply Properties of Rational Exponents to Simplify (6.2) 121/8 x 125/6 121/8+5/6 1223/24 (51/3 x 71/4)3 (51/3)3 x(71/4)3 5 x 73/4 (26 x 46)-1/6 2-1 x 4-1 = 1/8 (26 • -1/6 x 46 •-1/6) 10/102/5 103/5 101-2/5

Use Properties of Radicals to Simplify n√a•b = n√a •n√b √5•2 = 10 3√125 •3√8 3√125•8 5√96 5√3 5√32 = 2 4√27 • 4√3 4√27•3 4√81 = 3 33√5 3√135 3√27•5

Apply Properties of Rational Exponents to Add & Subtract 75√12-5√12 (7-1)5√12 65√12 4(92/3)+8(92/3) (4+8)(92/3) 12(92/3) 3√81- 3√24 33√3-23√3=3√3 3√27•3- 3√8•3 63√5+43√625 (6+20)3√5=263√5 63√5+43√5•125= 63√5+(4•5)3√5

Simplify Expressions Involving Variables 4√625z12 4√5•5•5•5•z4•z4•z4 5z3 (32m5n30)1/5 321/5m5/5n30/5 2mn6 3√6x4y9z14 xy3z43√xz2 3√6•x3•x1•y3•y3•y3•z3•z3•z3•z3•z2

Your Turn • P 424 • 4-8, 12, 24-26, 28, 32-35, 43-46, 52, 53 • Homework: Finish classwork problems

Evaluate nth Roots, Properties of rational exponents