Chapter 8.CM, Problem 1CM

To determine

To find:

The simplified form of the given expression.

Answer to Problem 1CM

Solution:

The simplified form of the given expression is $47$.

Explanation of Solution

Given:

The given expression is $4^3+\left[3^2-\left(10÷2\right)\right]-7\cdot 3$.

Calculation:

Here, the concept of BODMAS must be applied. According to this rule, the expression must be simplified in the following order:

1. Brackets:

• Curly brackets

• Square brackets

• Curved brackets

2. Off

3. Division

4. Multiplication

5. Addition

6. Subtraction

Applying BODMAS rule to the given expression:

On simplifying the brackets, the given expression transforms to:

$\begin{array}{l}{4}^3+\left[3^2-\left(10÷2\right)\right]-7\cdot 3\\ =4^3+\left[3^2-\left(10\times \frac{1}{2}\right)\right]-7\cdot 3\\ =4^3+\left[3^2-5\right]-7\cdot 3\\ =4^3+\left[9-5\right]-7\cdot 3\end{array}$

$=4^3+4-7\cdot 3$

After completing the ‘OFF’ operation, the given expression reduces to:

$=4^3+4-21$

Simplifying the expression further by multiplying $4$, three times:

$=64+4-21$

Adding the given two numbers:

$=68-21$

Finally, on subtracting the two numbers:

$=47$

Conclusion:

Thus, the simplified form of the given expression is $47$.