Chapter 2.1, Problem 20E

Solution

Find the value of ${\left(4.0\times {10}^3\right)}^4$ and property used.

The value of ${\left(4.0\times {10}^3\right)}^4$ is $2.56\times {10}^{14}$ and property used are product of power $a^m{a}^n=a^{m+n}$ and power of power ${\left(a^n\right)}^m=a^{nm}$ .

Given:

Expression: ${\left(4.0\times {10}^3\right)}^4$ .

Concept Used:

Property used are product of power $a^m{a}^n=a^{m+n}$ and power of power ${\left(a^n\right)}^m=a^{nm}$ .

Calculation:

The product of power and power of power are used to solve the question.

  $\begin{array}{c}{\left(4.0\times {10}^3\right)}^4=\left({\left(4.2\right)}^4\times {10}^{\left(3\times 4\right)}\right)\\ =256\times {10}^{12}\\ =2.56\times {10}^{14}\end{array}$

Thus, the final value is $2.56\times {10}^{14}$ .