Question

Simplify the following expression:
\[\left( \left( 4\times {{10}^{-2}} \right)-\left( 2.5\times {{10}^{-3}} \right) \right)\left( {{10}^{4}} \right)\]

Answer 1

Hint: Solve the whole expression according to the BODMAS rule. First, simplify both the brackets in the given expression individually and then do the remaining solution. Use \[{{a}^{-n}}=\dfrac{1}{{{a}^{n}}}\] in the first step to begin the solution.

Complete step-by-step answer:
Here we have to simplify the expression: \[\left( \left( 4\times {{10}^{-2}} \right)-\left( 2.5\times {{10}^{-3}} \right) \right)\left( {{10}^{4}} \right)\].
Before proceeding with this question, we must know what a BODMAS rule is. BODMAS is an acronym and it stands for Bracket Of Division, Multiplication, Addition, and Subtraction. It explains the order of the operations to solve an expression. The ‘of’ in the BODMAS full form is also called “Order”, which refers to the numbers which involve powers, square roots, etc. According to BODMAS rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by ‘of’ (powers, roots, etc.), then division, multiplication, addition and subtraction from left to right.
Let us consider the expression given in the question
\[E=\left( \left( 4\times {{10}^{-2}} \right)-\left( 2.5\times {{10}^{-3}} \right) \right).\left( {{10}^{4}} \right)\]
Let us solve each bracket individually. We know that \[{{a}^{-n}}=\dfrac{1}{{{a}^{n}}}\]. By using it in the above expression, we get,
\[E=\left( \left( \dfrac{4}{{{\left( 10 \right)}^{2}}} \right)-\left( \dfrac{2.5}{{{\left( 10 \right)}^{3}}} \right) \right).\left( {{10}^{4}} \right)\]
By further simplification of the above expression, we get,
\[E=\left( \left( \dfrac{4}{100} \right)-\left( \dfrac{2.5}{1000} \right) \right).\left( {{10}^{4}} \right)\]
\[E=\left( 0.04-0.0025 \right)\left( {{10}^{4}} \right)\]

By further simplifying the above expression, we get
\[E=\left( 0.0375 \right)\left( {{10}^{4}} \right)\]
Or, \[E=\left( 0.0375 \right)\left( 10000 \right)\]
So, we get E = 375.
Hence, the value of the expression \[\left( \left( 4\times {{10}^{-2}} \right)-\left( 2.5\times {{10}^{-3}} \right) \right)\left( {{10}^{4}} \right)\] is equal to 375.

Note: Students must note that they should always solve any equation according to the BODMAS rule. Solving the problem in the wrong order will result in the wrong answer. Also, if there is more than one bracket in any question, always first simplify the expression inside each bracket individually according to BODMAS rule and then do the remaining solution. All these points must be kept in mind to get the correct answer.