Chapter 1, Problem 10CR

To determine

To Evaluate: The expression $\frac{40-2^3}{4+3{\left(2\right)}^2}$

Answer to Problem 10CR

  $\frac{40-2^3}{4+3{\left(2\right)}^2}=2$

Explanation of Solution

Given information:

The expression $\frac{40-2^3}{4+3{\left(2\right)}^2}$

Concept and Formula Used:

Rule of exponent and addition and subtraction.

  $a^n=a\times a\times a\times \mathrm{..................}n\text{ times}\text{.}$

BODMAS rule

Calculation:

The given expression is $\frac{40-2^3}{4+3{\left(2\right)}^2}$

Evaluate the power in numerator and denominator

  $\begin{array}{l}\frac{40-2^3}{4+3{\left(2\right)}^2}=\frac{40-8}{4+3\left(4\right)}\\ \text{Now multiply 3 and 4}\\ \frac{40-2^3}{4+3{\left(2\right)}^2}=\frac{40-8}{4+12}\\ \text{On simplifying}\\ \frac{40-2^3}{4+3{\left(2\right)}^2}=\frac{32}{16}\\ \frac{40-2^3}{4+3{\left(2\right)}^2}=2\end{array}$

Conclusion:

  $\frac{40-2^3}{4+3{\left(2\right)}^2}=2$