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 (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.


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


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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