In this publication, we will consider how a number, an ordinary and a decimal fraction can be raised to a negative power. We will also analyze practical examples on this topic.
Rules for raising a number to a negative power
To fully master the material presented below, you need to know what a power of a number is and what properties it has. We discussed this issue in detail in a separate article.
Integer
Algorithm of actions:
- We represent the number as an ordinary fraction, in the numerator of which is one, and in the denominator – the original number.
- We change the negative degree to a positive one.
- Raise the resulting fraction to a power.
The general formula looks like this:
- a ≠ 0;
- n ∈ Z, i.e. set of integers.
examples:
Note: Any number raised to the power of zero equals one.
a0 = 1Where a ≠ 0
examples:
- 70 = 1;
- (-16)0 = 1.
Decimal
To raise a decimal to a negative power, follow the same steps as for integers.
examples:
Common fraction
To raise a fraction to a negative power, do the following:
- Swap the numerator and denominator;
- We replace the negative degree with a positive one;
- We raise both the numerator and the denominator to a power.
Notes:
- If the fraction is positive, then raising it to any power also gives a result greater than zero.
- If the sign of a fraction is negative, then when it is raised to an odd power, a negative fraction is obtained, and when it is raised to an even power, a positive one is obtained.
examples:
Note: an ordinary fraction can also be first converted to , and then exponentiated.
Example:
