# Power equations

A power equation refers to an equation that reduces to this form

Where the numbers *x* and* a* and* b* are such that the equation is defined.

The inverse of a power is a root.

The general solution to the above form is

For every power there is a corresponding root. The second power has a square root (a second root), the third power has a third root, and so on.

If *a* is even, there are two solutions. Then *b* must be positive.

If* a* is odd, there is only one solution and *b* can also be negative.

Example

The target is to reduce sulphur emissions from industrial plants by 60% in five years. What should the annual reduction target be?

Solution

We mark the amount of sulphur emissions by the letter* a* and the annual reduction *x*. After five years, only 40% remain.

We get the equation

0.833 = 83.3%, which means an annual reduction target of 100% -83.3% = 16.7%

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