Power equations
Sometimes a variable in an equation may include also an exponent, for example
An equation
where n is a positive integer and a is a real number, is called as a power equation. If n is an even natural number, then a must be at least zero. For odd n, there is no restrictions.
During this course, we are concentrating on positive solutions, so negative solutions can be omitted.
| n | a | x |
| even | nth rooth of a | |
| odd | any real number | nth rooth of a |
Example 1.
Only the square root and cube root are usually found from calculators. All the other roots can be solved with fraction power: