Question

How do you calculate \[\left( {{{3.10}^2}} \right)\left( {{{2.10}^3}} \right)\] ?

Answer 1

Hint: Here in this question we have given a number. The terms which involve this term are in the exponential form. Here we have braces and a dot symbol, this implies that we have to use the arithmetic operations. Hence on further simplification we obtain the required solution for the question.

Complete step-by-step answer:
The exponential number is defined as the number of times the number is multiplied by itself. It is represented as \[{a^n}\] , where a is the numeral and n represents the number of times the number is multiplied.
So now consider the given question
 \[\left( {{{3.10}^2}} \right)\left( {{{2.10}^3}} \right)\]
Let we expand the terms which are in the exponential form, so we have
 \[ \Rightarrow \left( {3.100} \right)\left( {2.1000} \right)\]
The dot represents the multiplication, so we multiply the terms we have
 \[ \Rightarrow \left( {300} \right)\left( {2000} \right)\]
The two terms in the above equation are in the braces. Suppose if a number are in braces we use the arithmetic operation multiplication. On multiplying the above two terms we get.
 \[ \Rightarrow 600000\]
We can also solve this by using another method.
So now consider the given question
 \[\left( {{{3.10}^2}} \right)\left( {{{2.10}^3}} \right)\]
By the law of indices we have \[{a^n}.{a^m} = {a^{n + m}}\] , we use this property to the above equation we have
 \[ \Rightarrow (3)(2){10^{2 + 3}}\]
On simplifying we have
 \[ \Rightarrow (3)(2){10^5}\]
The two terms in the above equation are in the braces. Suppose if a number are in braces we use the arithmetic operation multiplication. On multiplying the above two terms we get.
 \[ \Rightarrow {6.10^5}\]
Let we expand the terms which are in the exponential form, so we have
 \[ \Rightarrow 6.100000\]
The dot represents the multiplication, so we multiply the terms we have
 \[ \Rightarrow 600000\]
Hence we have solved the above equation and found the solution.
So, the correct answer is “600000”.

Note: The exponential number is defined as the number of times the number is multiplied by itself. It is represented as \[{a^n}\] , where a is the numeral and n represents the number of times the number is multiplied. For the exponential numbers we have a law of indices and by applying it we can solve the given number.