1. Warm-Up Honors Algebra 2 1/16/19
Simplify each expression. Assume that all variables are positive.
3 8 𝑥
𝑥 2 2 𝑥 𝑥 8 81

2. A rational exponent is an exponent that can be expressed as , where m and n are integers and n ≠ 0. Radical expressions can be written by using rational exponents. m n

3. The denominator of a rational exponent becomes the index of the radical.
Writing Math
𝑎 𝑚 𝑛 = 𝑛 𝑎 𝑚 𝑜𝑟 𝑛 𝑎 𝑚

4. Example 3: Writing Expressions in Radical Form
−𝟑𝟐 𝟑 𝟓
Write the expression in radical form and simplify.
Method 1 Evaluate the root first.
Method 2 Evaluate the power first. ( ) - 3 5 32
Write with a radical.
Write with a radical.
(–2)3
Evaluate the root.
Evaluate the power. - 5
32,768 –8
Evaluate the power. –8
Evaluate the root.

5. ( ) ( ) Write the expression 𝟔𝟒 𝟏 𝟑 in radical form, and simplify.
Check It Out! Example 3a
Write the expression 𝟔𝟒 𝟏 𝟑 in radical form, and simplify.
Method 1 Evaluate the root first.
Method 2 Evaluate the power first. ( ) 1 3 64
Write with a radical. ( ) 1 3 64
Write will a radical.
(4)1
Evaluate the root.
Evaluate the power. 3 64 4
Evaluate the power. 4
Evaluate the root.

6. ( ) Write the expression 𝟒 𝟓 𝟐 in radical form, and simplify. ( )
Check It Out! Example 3b
Write the expression 𝟒 𝟓 𝟐 in radical form, and simplify.
Method 1 Evaluate the root first.
Method 2 Evaluate the power first. ( ) 5 2 4
Write with a radical. ( ) 5 2 4
Write with a radical.
(2)5
Evaluate the root. 2
1024
Evaluate the power. 32
Evaluate the power. 32
Evaluate the root.

7. ( ) Write the expression 𝟔𝟐𝟓 𝟑 𝟒 in radical form, and simplify. ( )
Check It Out! Example 3c
Write the expression 𝟔𝟐𝟓 𝟑 𝟒 in radical form, and simplify.
Method 1 Evaluate the root first.
Method 2 Evaluate the power first. ( ) 3 4
625
Write with a radical. ( ) 3 4
625
Write with a radical.
(5)3
Evaluate the root. 4
244,140,625
Evaluate the power.
125
Evaluate the power.
125
Evaluate the root.

8. Example 4: Writing Expressions by Using Rational Exponents
Write each expression by using rational exponents. B. A. 4 8 13 = m n
a a = m n
a a 15 5 13 13 1 2
Simplify.
133
Simplify.
2197

9. Write each expression by using rational exponents.
Check It Out! Example 4
Write each expression by using rational exponents. a. b. c. 3 4 81 9 3 10 2 4 5
103
Simplify. 5 1 2
Simplify.
1000