evaluate nth roots and use rational exponents

Evaluate nth Roots and Use Rational

ExponentsAlgebra 2

32 = 9

102 = 100

2172 = 47089

Squares and Square Roots

23 = 8

53 = 125

1713 = 5000211

Cubes and Cube Roots

For an integer n greater than 1, if b n = a, then

The nth root of a is equal to b

General Rule

Rational Exponents

Let n be an integer (n > 1), a is a real number and

n is an even integer

a < 0, no real nth roots

a = 0, one real nth root

a > 0, two real nth roots

Real nth Roots of a

Let n be an integer (n > 1), a is a real number and

n is an odd integer

a < 0, one real nth root

a = 0, one real nth root

a > 0, one real nth root

Real nth roots of a

n = 5, a = -32

Answer, n is odd so there is 1 solution:

n = 6, a = 1

Answer – n is even, a is positive so 2 solutions:

Find the real nth root(s) of a

Rational exponents don’t have to be in the form 1/n

Rational Exponents

125 2/3

Answer : 125 2/3 = (125 1/3)2 = 52 = 25

8 -4/3

Answer: 1/16

Evaluate each expression

Solve: 4x5 = 128

Solve: (x – 3)4 = 21

Solve: x6 – 34 = 181

Solving Equations

Solve: 4x5 = 128 x = 2

Solve: (x – 3)4 = 21 x=

Solve: x6 – 34 = 181 x=

Solving Equations

If an expression is irrational then the solution or simplification can be expressed two ways:

Exact answer:

Approximate answer:

Rational Exponent Example

Approximating Roots