Question

How do you simplify \[( - 1)\] to the \[{\text{5th}}\] power?

Answer 1

Hint: Here in this question we are asked to simplify \[( - 1)\] to the \[{\text{5th}}\] power which means \[{( - 1)^5}\] where \[( - 1)\] constant positive power which has \[5\] . Here in this case the factor which is multiplied repeatedly is \[( - 1)\] also known as base while \[5\] is the power representing the repeated multiplication of a number. So it means we multiply \[( - 1)\] five times.
Formula: The formula used for solving the above question will be based on general formula of multiplication which is
 \[{(a)^n} = a \times a \times a \times a \times a...... \times a({\text{n times)}}\]
It is a simplified method of repeated multiplication and use the correct rule to split the terms and simplify the answer.

Complete step by step solution:
So here let’s assume that a constant \[a\] has to be multiplied by itself \[n{\text{ times}}\] . Thus it can be written as \[{(a)^n}\] in the exponential form instead of writing it as \[a \times a \times a \times a \times a...... \times a({\text{n times)}}\]
As we need to simplify \[{( - 1)^5}\]
So it means we need to multiply \[( - 1)\] five times
 \[{( - 1)^5} = ( - 1) \times ( - 1) \times ( - 1) \times ( - 1) \times ( - 1) = - 1\]
It will give the final answer is \[ - 1\] as an odd number of negatives gives the answer negative.
So, the correct answer is “-1”.

Note: Keep in mind that while multiplying a term (constant or variable) with itself for multiple times it can be represented as exponential form more easily and in a more readable format. While solving the above problem and multiplying it, remember that an odd number of negatives give the answer negative. If the number is given with power \[n\] then it can be written \[n\] times a number. Students must remember the rules of exponents while simplifying such problems and need to be careful during application of rules.