LEQ: What is the process used to simplify expressions or solve equations with exponents of the form 1/n?

 Recall: x is a square root of t if and only if x 2 = t.  Similarly, x is a cube root of t if and only if x 3 = t. ◦ For example: 4 is a cube root of 64 because 4 3 = 64  Definition: Let n be an integer greater than 1. Then b is an n th root of x if and only if b n = x.

 The real n th roots of a number can be estimated from a graph. ◦ For example: Estimate the real 12 th roots of 2.  The real 12 th roots of 2 are the real solutions to x 12 = 2.  Enter x 12 in Y1 and 2 in Y2.  Calculate the points of intersection.  2 nd, TRACE, 5  x ≈ and

 1/n Exponent Theorem ◦ When x ≥ 0 and n is an integer greater than 1, x 1/n is an n th root of x.  x 1/2 is the positive square root of x  2 1/3 is the positive cube root of 2  81 1/4 is the positive fourth root of 81  x 4 = 81  x = 3

 Every positive real number has: ◦ 2 real n th roots, when n is even ◦ 1 real n th root, when n is odd  Every negative real number has: ◦ 0 real n th roots, when n is even ◦ 1 real n th root, when n is odd

 Find all real solutions to x 5 = 80. ◦ To get the x alone, raise both sides to the 1/5 power. ◦ (x 5 ) 1/5 = (80) 1/5 ◦ x = 2.402

 Lesson Master 7-6A #1, 3, 5, 8, 11, 12, 14, 15

 Pgs #5, 6, 8, 9, 12-20, 25-30, 32, 33