Question

How do you simplify $ {{(4t)}^{3}} $ ?

Answer 1

Hint: The given expression is an algebraic expression. In order to simplify an algebraic expression, the power to which the base is raised denotes the number of times a base needs to be multiplied by itself.

Complete step by step answer:
Let us first understand an example before moving onto the question. Consider an algebraic expression $ {{a}^{3}} $ , here $ a $ is the base and $ 3 $ is the power. It means here in order to simplify $ {{a}^{3}} $ , $ a $ needs to be multiplied 3 times by itself as $ a\times a\times a $ . Likewise, here in this question in order to simplify $ {{(4t)}^{3}} $ the base $ 4t $ needs to be multiplied 3 times by itself. By doing so, the given algebraic expression will be simplified.
The given algebraic expression is $ {{(4t)}^{3}} $ .
To simplify it, we need to multiply it $ 3 $ times by itself and we get,
 $ \Rightarrow 4t\times 4t\times 4t $
We can rearrange the above expression as given below
 $ \Rightarrow (4\times 4\times 4)(t\times t\times t) $
 $ \Rightarrow 64{{t}^{3}} $
Hence the simplified form of the above given algebraic expression is $ 64{{t}^{3}} $.

Note:
 Be careful and attentive while you deal with the algebraic expression. The most common mistake which is made in such questions is the basic mathematical operations. For example, in the above question, the student instead of multiplying the base $ 4t $ three times by itself, multiply the base $ 4t $ by $ 3 $, and the solution goes wrong. Hence one should understand the meaning of the question properly. Many times students do not use brackets and parentheses properly in their respective places and get confused with the question. So Always use the correct brackets and parentheses at the right place in an algebraic expression to solve a question.