1.6 E) Negative Powers
Negative Powers
When we have negative powers (e.g. 7-2) we reciprocate it and make the power positive. Reciprocating means that you turn the number the other way up; the numerator will be the denominator and the denominator (which is usually 1) will be the numerator. Here are a few examples of numbers/ unknowns and their reciprocals:
> 4 has the reciprocal ¼
> 10 has the reciprocal 1/10
> 25 has the reciprocal 1/25
> x has the reciprocal 1/x
> 21y has the reciprocal 1/21y
When we have reciprocated the number with a negative power, we then make the power positive.
Example 1
What is:
The first step is to reciprocate it and then change the power from a negative to a positive power. This gives us:
7 now has a positive power of 2, which means that we square 7.
72 is 49. Therefore, we can write the answer as 1/49.
The key rule with a negative power is to reciprocate it and then change the power to a positive power.
Example 2
What is:
We need to reciprocate this and then make the power positive. This means that we need to work out.
You will rarely see a negative power in the denominator of an exam, but if you do the process is exactly the same; you find the reciprocal (flip the numerator and the denominator) and then make the power positive.
Example 3
What is:
We need the flip the fraction to find the reciprocal and then make the power positive.
Anything divided by 1 is just itself.