Chapter 7.3, Problem 32P

Simplify. Write each answer in scientific notation.

${\left(3\times {10}^{-8}\right)}^3$

To determine

To find: The scientific notation of the provided expression.

Answer to Problem 32P

The scientific notation is $2.7\times {10}^{-23}$

Explanation of Solution

Given:

The expression is:

  ${\left(3\times {10}^{-8}\right)}^3$

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:

  $\begin{array}{c}{\left(3\times {10}^{-8}\right)}^3=3^3\times {\left({10}^{-8}\right)}^3\\ =3^3\times \left({10}^{-24}\right)\\ =27\times {10}^{-24}\\ =2.7\times {10}^{-23}\end{array}$

Thus, the required solution is $2.7\times {10}^{-23}$ .