Formulas for powers
All formulas are written below. If you have a formula book in use, please, check how they are written there.
Based on these formulas: and We can check the first with example
Example 1.
In both cases, the power is an even number. This means that the result of a negative number raised to an even power is always a positive number.
In these cases, the power is an odd number, i.e the result of a negative number raised to an odd power is a negative number.
Example 2.
If the next problem had to be calculated without a calculator, then raising the numbers to the power and then multiplying them makes the numbers too large to calculate in your head. When the numbers in the denominator are converted to the power form, the "unnecessary" ones can be reduced and calculation in the head is easier.
In the field of technology, you often have to work with parameters/variables (="letters"). In this case, the calculator is not even as useful as when calculating with numbers. On the other hand, all the terms have already been given with the help of powers and the cancellation can be done right away. Below is the same task when numbers are not given:
Remember that cancellation is only possible when the numbers or terms are multiplied!
Example 3.
Example 4.
Example 5.