Download 5-5 Reteaching

Name
Class
Date
Reteaching
5-5
Rational Exponents and Radicals
When you understand the equivalence of radicals and rational exponents, you
can represent a radical expression using rational exponents.
If the nth root of a is a real number and m and n are positive integers, then
1
n
n
a = a and a
m
n
n
= a
m
You can also represent an expression with rational exponents as a radical
expression. Sometimes converting from one form to the other makes it easier to
simplify an expression involving roots.
Problem
3
2
What is 8 in radical form? Simplify, if possible.
2
3
3
Rewrite the expression in radical form.
3
Simplify.
8 = 82
= 82 = 3 64 = 3 4 • 4 • 4 = 4
Write each expression in radical form, then simplify if possible.
1. 36
1
5
2
5
2
2
3
4. 18b 3
2. 4
3.
(27 x)
Problem
What is
4
(16 x)3 in exponential form? Simplify, if possible.
3
4
3
(16 x ) = (16 x)
3
4
3
Rewrite the expression in radical form.
3
= 16 4 x 4 = 8 x 4
Simplify.
Write each expression in exponential form, then simplify if possible.
5.
3
82
6.
3
8x
7.
3
64x 7
Pearson Texas Algebra I
8.
3
(27 x) 2
Name
Class
5-5
Date
Reteaching (continued)
Rational Exponents and Radicals
You can use the properties of exponents to simplify expressions with rational
exponents. When simplifying radical expressions, you can combine like terms.
Problem
⎛ 1⎞ ⎛ 1⎞
What is the simplified form of the expression, ⎜ a 4 ⎟ ⎜ a 4 ⎟ ? Use the properties of
⎝ ⎠⎝ ⎠
exponents, and then write the expression in radical form.
1
1
+1
⎛ 14 ⎞ ⎛ 14 ⎞
4
4
= a2
⎜a ⎟ ⎜a ⎟ = a
⎝ ⎠⎝ ⎠
=
When multiplying like bases, add the exponents.
a
Rewrite in radical form.
Simplify each expression using the properties of exponents, and then write the
expression in radical form.
9.
⎛ 23 ⎞ ⎛ 1 ⎞
4
⎜a ⎟ ⎜a ⎟
⎝ ⎠⎝ ⎠
10. ( ab ) 3 ⎜ b 2 ⎟
11.
⎛ 15 ⎞ 2
⎜ 5x ⎟ ( x )
⎝ ⎠
12. (8 x ) 3 (64 x ) 2
1
⎛
1
⎝
⎞
⎠
1
1
Problem
What is the exponential form of the expression,
3
3
5
a3 + 3 a5 ?
5
a + 3 a = a + 3a 2
2
Rewrite the expression in exponential form. The expression
cannot be simplified further because the terms are not
like terms.
Write each expression in exponential form. Simplify when possible.
3
( 16 x )+ ( 27 x )
13.
3
a2 + 2 a2
14.
15.
3
(27 x) 2 + 4 256 x 2
16. 4 3 (3 x ) −
3
4
6
Pearson Texas Algebra I
(2 x) 4
5