Question

How do you evaluate the power \[{{5}^{3}}\] ?

Answer 1

Hint: In the above question we have a simple exponential expression. In order to solve it we will apply simple exponential rules. As we can see that the number 5 is raised to the power 3. This means we have to multiply the base by itself three times.

Complete step by step answer:
Let us first understand an example before solving the question. Consider an exponential expression \[{{a}^{3}}\] , here \[a\] is the base whose value is known and 3 is the power or the index to which the base is raised. 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 \[{{5}^{3}}\] the base \[{{5}^{3}}\] needs to be multiplied 3 times by itself. By doing so, the given exponential expression will be simplified.
The given algebraic expression is \[{{5}^{3}}\] .
To simplify it, we need to multiply it 3 times by itself
\[\Rightarrow 5\times 5\times 5\]
On solving further, we get
\[\Rightarrow 125\]
Hence the solution for the above exponential expression is \[125\] .

Note:The most common mistake which is made in such types of questions is the basic mathematical operations which are multiplication, addition and subtraction. Also keep in mind that in the above question we have to multiply the base three times not the base value and the power. Always use the correct brackets and parentheses at the right place in an exponential expression to solve a question. Be careful while solving these types of questions.