Chapter 1.2, Problem 13P

Simplify each expression.

${(4(5))}^3$

To determine

To Simplify: The expression ${\left(4\left(5\right)\right)}^3$

Answer to Problem 13P

The value of the expression ${\left(4\left(5\right)\right)}^3$ is $8000$

Explanation of Solution

Given information:

The expression ${\left(4\left(5\right)\right)}^3$

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

  $\begin{array}{l}{\left(4\left(5\right)\right)}^3\\ \text{Simplifying the product inside the bracket}\\ {\left(4\left(5\right)\right)}^3={\left(20\right)}^3\\ \text{Using }{a}^n=a\times a\times a\times \mathrm{..................}n\text{ times}\\ {\left(4\left(5\right)\right)}^3=20\times 20\times 20\\ {\left(4\left(5\right)\right)}^3=8000\end{array}$

Conclusion:

The value of the expression ${\left(4\left(5\right)\right)}^3$ is $8000$