Question

Evaluate $ {\left( 8 \right)^3} $
(A) $ 256 $
(B) $ 64 $
(C) $ 8 $
(D) $ 512 $

Answer 1

Hint: In this question we are asked to find the value of $ {\left( 8 \right)^3} $ . Here $ 8 $ is a whole number and we will find the cube of $ 8 $ . For this purpose, we will multiply $ 8 $ three times by itself. So first we are going to evaluate the square of $ 8 $ and then multiply the square number by $ 8 $ again.

Complete step-by-step answer:
 Now we find out the value of $ {\left( 8 \right)^3} $ .
First let us calculate the square of $ 8 $ i.e., $ {\left( 8 \right)^2} $ .
Now $ {\left( 8 \right)^2} = 8 \times 8 $
i.e., $ {\left( 8 \right)^2} = 64 $ .
Now we shall multiply $ 8 $ to $ {\left( 8 \right)^2} $ and the value we obtain will be of $ {\left( 8 \right)^3} $ .
Therefore, $ {\left( 8 \right)^3} = {\left( 8 \right)^2} \times 8 $
 $ = 64 \times 8 $
 $ {\left( 8 \right)^3} = 512 $
Again, we can solve it in another way where we shall just multiply three $ 8 $ with each other.
So, $ {\left( 8 \right)^3} = 8 \times 8 \times 8 $ i.e., $ {\left( 8 \right)^3} = 512 $ .
So, the correct answer is “Option A”.

Note: Already we have mentioned one term, “whole number.” A whole number refers to the set $ \left\{ {0,1,2,3,4,5,...} \right\} $ i.e., it is the combined set (or union) of the natural numbers (the collection of all positive integers) and $ 0 $ . A number must not be negative and it will never carry a fractional part.
Another thing that students should remember, the definition of power to a number. Let “ $ a $ ” be any number and the question given is to find $ {a^n} $ where $ n $ is a natural number. To find these, the simplest and best process is to multiply the number $ a $ with itself $ n $ times.
Therefore $ {a^n} = a \times a \times a \times a \times ... \times a $ ( $ n $ times).
Students should remember this method so that they can easily evaluate any problem of this kind.