Unit 2 Day 5

Do now Fill in the blanks: is read as “___________________________” The 4 th root can be rewritten as the ________ power. If an expression has a rational (aka __________) exponent, then we can think of that exponent as “___________ over __________” to rewrite the expression in radical form.

Remember the rules for exponents? Multiplying with like bases: x m x n = ______ Dividing with like bases: = ______ Power to a power: (x m ) n = _______ Product to a power: (xy) m = ______ Quotient to a power: = _______ Zero power: x 0 = _______ Negative exponent: x - m = _______ These rules still work even if the exponents are rational numbers (fractions)!

Products and Quotients What if the exponents are rational numbers (fractions)? Rewrite using radicals. Product property: (xy) 1/n = x 1/n y 1/n  Ex. 1: Quotient property:  Ex. 2:

Ex. 3: Using Properties of Rational Exponents Simplify the expressions. a. 5 1/2  5 1/4 b. (x 1/2  y 1/3 ) 2 c. (2 4  3 4 ) -1/4

Ex. 4: Simplify the expression. a. b. c. d.

Ex. 5: Getting a Common Base Simplify the expressions. a. 2 1/2  8 1/4 b. (27 1/4  3 1/3 ) 2 c. (4 3  2 3 ) -1/3 d.

Ex. 6: Simplify the expression. a. b. c. d.

Simplest Form Rewriting radicals in simplest form Apply the properties of radicals Remove any perfect n th powers Rationalize any denominators

Evaluating Expressions with Rational Exponents We can use these ideas to evaluate expressions with fractional exponents. 25) Evaluate 9 1/2 Rewrite using radical notation: 26) /3 27) 1,000,000 1/6 Taking the root first is easier (smaller numbers)

Writing radicals in simplest form Is it divisible by any perfect n th powers? a. 29) (x 6 ) 1/2 30) (9n 4 ) 1/2 31) (64n 12 ) -1/6