1. 5.2 Apply Properties of Rational Exponents
Do properties of exponents work for roots?
What form must they be in?
How do you know when a radical is in simplest form?
Before you can add or subtract radicals what must be true?

2. Properties of Rational Exponents

3. Now see what changes I made…
This is a good example I why I have been complaining about the book slides. This is how it copies…
Use the properties of rational exponents to simplify the expression.
a /4 71/2
= 7(1/4 + 1/2)
= 73/4
b. (61/2 41/3)2
= (61/2)2 (41/3)2
= 6(1/2 2) 4(1/3 2)
= /3
= 6 42/3 1 12 =
c. (45 35)–1/5
= [(4 3)5]–1/5
= (125)–1/5
= 12[5 (–1/5)]
= 12 –1 d. 5
51/3 51
51/3 =
= 5(1 – 1/3)
= 52/3 = 42 6
1/3 2 e.
421/3 2
61/3
= (71/3)2
= 7(1/3 2)
= 72/3
Now see what changes I made…

4. Use the properties of rational exponents to simplify the expression.
= 7(1/4 + 1/2)
= 73/4
b. (61/2 • 41/3)2
= (61/2)2 • (41/3)2
= 6(1/2 • 2) • 4(1/3 • 2)
= 61 • 42/3
= 6 • 42/3
c. (45 • 35)–1/5
= [(4 • 3)5]–1/5
= (125)–1/5
= 12[5 • (–1/5)]
= 12 –1 1 12 = d. 5
51/3 51
51/3 =
= 5(1 – 1/3)
= 52/3 = 42 6
1/3 2 e.
421/3 2
61/3
= (71/3)2
= 7(1/3 • 2)
= 72/3

5. Write the expression in simplest form
You need to rationalize the denominator—no tents in the basement

6. Adding and subtracting like radicals and root.
When adding or subtracting like radicals the root and the number under the radical sign must be the same before you can add or subtract coefficients.
Radical expressions with the same index and radicand are like radicals.
You may need to simplify the radical before you can add or subtract.

7. Adding & Subtracting Roots and Radicals

8. Simplify the expression involving variables

9. Write the expression in simplest form

10. Add or subtract the expression involving variables.

11. Do properties of exponents work for roots?
Same rules apply.
What form must radical be in?
Fractional exponent form
How do you know when a radical is in simplest form?
When there are no more numbers to the root power as factors of the number under the radical.
Before you can add or subtract radicals what must be true?
The number under the radicals must be the same.