Fractional Exponents

1
Fractional Exponents
2
Careful!

• Calculate the following in your calculator

Not Exact
2 ( 1 2 )
3
A Math Trick to Evaluate 2½ Exactly

• Evaluate the following using our rules
• 21/2.21/2

21/2 1/2
21
2
4
What Does 2½ Exactly Equal?

• The final answer makes sense because

What is the number whose square is 2 x2 2 ?
5
Irrational Numbers

• Radical numbers/Fractional Roots are typically
  irrational numbers (unless they simplify to an
  integer). Our calculator gives

But the decimal will go on forever because it is
an irrational number. For the exact answer just
use
6
More Fractional Exponents

• Change the following into a radical
• 21/3

Remember 21/2 is also called the square root of 2
The cube root of 2. The solution to x3 2
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nth Roots

• The nth root of a number x is a number r which,
  when multiplied by itself n times equals x.

Examples
8
Radical v. Exponential Notation

• Rewrite the following roots as an exponential
  expression

9
Square Root Notation

• Remember

The 2 is implied!
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Roots in the Calculator
Exponential Notation
1
2

(
1

6
)
Radical Notation
(
6
)
(
1
2
)
MATH
is found in 5
11
What Does 25/3 Exactly Equal?
25/3
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Exponents into Radical Notation

• bp/q

Generally b0
13
Example
Evaluate the following without a calculator