Question

what will the sign of the product of the following a)28 times of the negative integers b) 13 times of the negative integers ​

Answer 1

Given :  product of the a)28 times of the negative integers b) 13 times of the negative integers ​

To find : sign of the product

Soution:

Negative integer  - x

can be written as (-1) * (x)   where x is + ve

i.e  (-1) ( magnitude of integer )

product of  28 times of the negative integers  

= (-1)²⁸ *  multiplication of  magnitude of integers

= ((-1)²)¹⁴ * multiplication of  magnitude of integers  

= (1)¹⁴ * multiplication of  magnitude of integers  

= (+ve)(+ve)

= + ve

28 times of the negative integers  is  + Ve

product of  13 times of the negative integers  

= (-1)¹³  *  multiplication of  magnitude of integers

= ((-1)²)⁶ * (-1)  * multiplication of  magnitude of integers  

= (1)⁶ * (-1)  * multiplication of  magnitude of integers  

= (+ve)(-1)(+ve)

= + ve (-1)

= - ve

13 times of the negative integers  is  - Ve

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what will the sign of the product of the following

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Answer 2

DETERMINING THE SIGN OF THE PRODUCT

We are asked that what will be the sign of the product of :-

• 28 times of a negative integer
• 13 times of a negative integer

Solution :-

Let the given negative integer be (-x)

It can also be written as (-1) * x.

(1)

= (-1)²⁸ * x²⁸

= ((-1)²)¹⁴ * x²⁸

= (1)¹⁴ * x²⁸

= 1 * x²⁸

Now, we know that (+,+) = +

Therefore, the sign of the product of 28 times of a negative integer is positive.

(2)

= (-1)¹³ * x¹³

= ((-1)²)⁶ * (-1) * x¹³

= (1)⁶ * (-1) * x¹³

= 1 * (-1) * x¹³

Now we know that (+,-,+) = -

Therefore, the sign of the product of 13 times of a negative number is negative.

Note :- If the power of the negative number is even then the sign of the product is positive whereas if the power of the negative number is odd then the sign of the product is negative.