1. Fractional Exponents and Radicals

2. Fractional Exponents: Calculator Warning
Calculate the following in your calculator:
Not Exact. What is the exact value of 21/2?
2 ^ ( 1 ÷ 2 )

3. A Math Trick to Evaluate 2½ Exactly
Evaluate the following using Exponential Laws:
21/2.21/2
When multiplying, if the bases are the same add the exponents
21/2 + 1/2 = 21 2
Now use this result to figure out what
21/2 equals.

4. What Does 2½ Exactly Equal?
Since:
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

7. 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!

10. Roots in the Calculator
Exponential Notation: 1 2 ^ ( 1 ÷ 6 )
Radical Notation: ( 6 ) ( 1 2 )
MATH
is found in #5

11. Fractional Exponents with Numerators greater than 1
Approximate the following expression:
25/3 ≈
Find the exact value:
Expand
Rewrite in Radical Notation
Simplify

12. Exponential v. Radical Notation
bp/q =
Generally b≥0

13. Example Evaluate the following without a calculator:
Rewrite in Radical Notation
Simplify
By rewriting the fractional exponential expression into a radical expression, the arithmetic is more straightforward.