Chapter 7.3, Problem 36P

Simplify. Write each answer in scientific notation.

${\left(6.24\times {10}^{13}\right)}^3$

To determine

To find: The scientific notation of the provided expression.

Answer to Problem 36P

The scientific notation is $2.429\times {10}^{41}$

Explanation of Solution

Given:

The expression is:

  ${\left(6.24\times {10}^{13}\right)}^3$

Concept used:

The scientific notation of large numbers is:

  $\begin{array}{l}a\times {10}^n\\ \text{Here,}\\ a\text{ lies between 1 and 10}\\ n\text{ is an integer}\end{array}$

Calculation:

The provided expression could be simplified as:

  $\begin{array}{c}{\left(6.24\times {10}^{13}\right)}^3={\left(6.24\right)}^3\times {\left({10}^{13}\right)}^3\\ =\left({1.7}^3\times {10}^{39}\right)\\ =242.9\times {10}^{39}\\ =2.429\times {10}^{41}\end{array}$

Thus, the required notation is $2.429\times {10}^{41}$ .