For the rest of this chapter, it will be assumed that all variables represent non-negative real numbers.
So,
 = a, a  0.
- Radical to Exponential Form
- For a 0 and n > 0
 = a1/n
 = am/n
 = an/n = a
- Exponential to Radical Form
- For a 0 and n > 0
am/n = 
- Rules of Exponents
- The rules of exponents are the same as were given in Chapter 5, section 1.
The rules of exponents apply to rational numbers in the exponents.
- Factoring
- When factoring out the greatest common factor, take out the smallest exponential power of any factors that are common to all terms.
| Example: |
x-2 + x2 = x-2(1 + x4) = |
1 + x4
x2 |
- Also, look for expressions that are in quadratic form, that are then easily factored.
This was done in Chapter 6, section 2.
| Example: |
| |
x4/3 + 2x2/3 + 1 |
| = |
(x2/3)2 + 2(x2/3) + 1 |
| |
Letting y = x2/3, then |
| = |
y2 + 2y + 1 |
| = |
(y + 1)2 |
| |
Substituting x2/3 back in for y, gives |
| = |
(x2/3 + 1)2 |
|
