Download bb = b 16 162 38 = p 8

Algebra
Date _________
Chapter 7 Exponents and Exponential Functions
7-3 Rational Exponents
N.RN.1 Explain how the definition of the meaning of rational exponents follows form
extending the properties of integer exponents to those values, allowing for a notation for
radicals in terms of rational exponents
N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties
of exponents.
Vocabulary
Rational exponent –
Cube root-
Nth root –
Exponential equation –
Key Concept: b
1
2
1
Words: For any nonnegative real number b, b 2 = b
Examples: 16
1

2
16
1
2
38 
38
Example 1: Radical and Exponential Forms
Write each expression in radical form, or write each radical in exponential form.
1
a) 25 2
b) 5x
1
2
c) 18
d)
8p
Key Concept: nth Root
Words: For any real numbers a and b and any positive integer n if an=b, then a is an nth root of b.
Symbols: If an = b then
n
b a
Example: Because 24=16, 2 is a fourth root of 16,
4
16  2
Example 2 nth roots
Simplify.
a)
3
b)
27
Key Concept: b
5
32
1
n
1
n
Words: For any positive real number b and any integer n> 1, b = n b
1
Example: 8 3  3 8  3 2  2  2or 2
1
n
Example 3 Evaluate b Expressions
Simplify
a) 125
1
3
b) 1296
1
4
m
Key Concept: b n
m
Words: For any positive real number b and any integers m and n> 1, b n = ( n b) m
2
Example: 8 3  ( 3 8 ) 2 = 22 = 4
m
n
Example 4 Evaluate b Expressions
Simplify
2
3
a) 64 3
b) 36 2
Key Concept: Power Property of Equality
Words: For any real number b> 0 and b  1, b x b y if and only if x=y.
x
3
n
Examples: If 5 =5 , then x=3, if n= ½ , then 4 =4
1
2
Example 5 Solve Exponential Equations
Solve each equation.
a)
6x = 216
b) 25x-1 = 5
Example 6 Solve Exponential Equations
It is important to protect your skin with sunscreen to prevent damage. The sun protection
factor (SPF) of a sunscreen indicates how well it protects you. Sunscreen with an SPF of f
absorbs about p percent of the UV=B rays where p =50f
100% of UV-B rays.
50.2
. Find the SPF that absorbs