Question

Find the cube of the following number: $ -13 $

Answer 1

Hint: Cube of a number is product of the number by itself three time i.e., lets a random variable Z, then cube of Z will be represented by \[{{Z}^{3}}\]and will be calculated by the product of Z three times - $ Z\times Z\times Z $ this will lead to the solution.

Complete step-by-step answer:
As we know the cube of a variable is triple multiplication that number by itself.
In the given question we have to calculate the cube of $ -13 $ .
As said, it would be $ -13\times -13\times -13 $ .
While multiplying positive sign the power of the number does not concern the sign of the end result as $ +\times +=+ $ (a positive number when multiplied by another positive number the output is positive as well).
But when multiplying negative signs this is not the case as $ -\times -=+ $ so the end result of multiplication of two negative numbers is a positive number.
Only other cases left are $ +\times -=- $ and $ -\times +=- $ so as given when a positive number is multiplied by a negative number the outcome is a negative number.
So, in the given question cube of $ -13 $ is defined as $ {{(-13)}^{^{3}}} $
Which can be rewritten as $ -13\times -13\times -13 $ , which can be approached as a square of $ -13 $ being multiplied with $ -13 $ .
So, $ -{{13}^{2}}\times -13=-{{13}^{3}} $ .
Result of $ -{{13}^{2}} $ is $ -13\times -13=+169 $
Now the cube of $ -13 $ is $ +169\times -13 $ , which is $ -2197 $ .
So, cube of $ -13 $ is $ -2197 $
So, the correct answer is “ $ -2197 $ ”.

Note: Multiplication of positive numbers results in a positive outcome where multiplication between two negatives will result in a positive outcome but when three negative numbers are multiplied it is similar to a positive number being multiplied with a negative number which gives us a negative outcome.