7.3 Binomial Radical Expressions7.4 Rational Exponents

Objectives:

1.To add and subtract radical expressions.

2. To multiply and divide radical expressions.

3. To simplify expressions with rational exponents.

Example 1: Simplifya) b)

c)

Example 2: Simplifya) b)

Example 3: Multiplya) b)

Example 4: Rationalize the denominator.

a)

Trivia…

1. In what year was Barbie 1st created?1959

2. What TV star did 500,000 people show up to watch sing at the Berlin Wall?

Rational Exponents Roots can be written as fractional exponents.

Example 5: Write each root as a fractional exponent.

a) b) c) d)

Rational Exponents We can also go the opposite way and write

fractional exponents as roots.

Example 6: Write each fractional exponent as a root.

a) b) c) d)

Simplify.a)

Sometimes rewriting fractional exponents as radicals is beneficial.

b)

Example 7: Rewrite as radicals and simplifya) b) c)

Definition of a Rational Exponent

Write as a radical:

The denominator is the index of the radical(tells what root you have: square root, cube root, fourth root, etc.)

The numerator is the exponent.

Example 8: Rewrite in Radical Forma) b) c)

Example 9: Rewrite in Exponential Form

a) b) c)

Negative Exponents Remember from Algebra 1, to make a

negative exponent positive just move it from the numerator to the denominator or vise versa.

Make all exponents positive:

Example 10: Simplify (means no negative exponents)a) b) c)

Trivia…

1. In Aladdin, what was the name of Aladdin’s mischievous monkey? ABU

2. What Adam Sandler comedy featured Bob Barker's screen debut?

Happy Gilmore

Example 11: Simplifya) b) c)

Example 11: Simplifyd) e)

Homework P 382 – 383: 1, 5-11 odd, 15, 21, 23, 25 P 388 – 389: 31 – 49 odd, 59, 61, 69 – 75 odd