Question

Simplify and give reasons: \[{\left( { - 2} \right)^7}\]
A.\[ - 128\]
B.\[128\]
C.\[28\]
D.None of these

Answer 1

Hint: To solve this question we have to multiply \[ - 2\] seven times and write the answers. As we know that if a negative integer is multiplied by a negative integer then that number becomes positive. If a negative integer is multiplied by a positive integer then the answer to that number is also negative. So if \[ - 2\] is multiplied \[7\] times, the sign with the answer will be negative.

Complete step-by-step answer:
We have to find the value of \[{\left( { - 2} \right)^7}\]
On expanded version we write \[{\left( { - 2} \right)^7}\] in :
\[{\left( { - 2} \right)^7} = - 2 \times - 2 \times - 2 \times - 2 \times - 2 \times - 2 \times - 2\]
We know that if negative number is multiplied by negative number them answer is a positive number
\[{\left( { - 2} \right)^7} = \left( { - 2 \times - 2} \right) \times \left( { - 2 \times - 2} \right) \times \left( { - 2 \times - 2} \right) \times \left( { - 2} \right)\]
So \[\left( { - 2 \times - 2} \right)\] becomes 4
\[{\left( { - 2} \right)^7} = 4 \times 4 \times 4 \times \left( { - 2} \right)\]
On further solving
\[{\left( { - 2} \right)^7} = 64 \times \left( { - 2} \right)\]
We know that if positive number is multiplied by negative number them answer is a negative number
\[{\left( { - 2} \right)^7} = - 128\]
The value of the given expression \[{\left( { - 2} \right)^7}\] is
\[ \Rightarrow {\left( { - 2} \right)^7} = - 128\]
So, the correct answer is “Option A”.

Note:
I.If the power on a negative number is an odd number then the final answer is a negative number.
II.If the power on a negative number is an even number then the final answer is a positive number.
III.If power on a positive number is given then the answer of that expression is always positive irrespective of that number. Irrespective of the number that is even or odd.