Chapter 1.2, Problem 12P

Simplify each expression.

${\left(\frac{27-12}{8-3}\right)}^3$

To determine

To Simplify: The expression ${\left(\frac{27-12}{8-3}\right)}^3$

Answer to Problem 12P

The value of the expression ${\left(\frac{27-12}{8-3}\right)}^3$ is $125$ .

Explanation of Solution

Given information:

The expression ${\left(\frac{27-12}{8-3}\right)}^3$

Concept and Formula Used:

Rule of exponent and addition and subtraction.

  $a^n=a\times a\times a\times \mathrm{..................}n\text{ times,}\sqrt[n]{a}={\left(a\right)}^{\frac{1}{n}}\&{\left(a^m\right)}^n=a^{mn}$

Calculation:

The given expression is

  $\begin{array}{l}{\left(\frac{27-12}{8-3}\right)}^3\\ \text{Simplifying the subtraction inside the bracket}\\ {\left(\frac{27-12}{8-3}\right)}^3={\left(\frac{15}{5}\right)}^3\\ {\left(\frac{27-12}{8-3}\right)}^3={\left(5\right)}^3\left(\text{Simplify}\right)\\ \text{Using }{a}^n=a\times a\times a\times \mathrm{..................}n\text{ times}\\ {\left(\frac{27-12}{8-3}\right)}^3=5\times 5\times 5\\ {\left(\frac{27-12}{8-3}\right)}^3=125\end{array}$

Conclusion:

The value of the expression ${\left(\frac{27-12}{8-3}\right)}^3$ is $125$