Chapter 7.3, Problem 34P

Simplify. Write each answer in scientific notation.

${\left(9.3\times {10}^{-6}\right)}^{-2}$

To determine

To find: The scientific notation of the provided expression.

Answer to Problem 34P

The scientific notation is $1.16\times {10}^{10}$

Explanation of Solution

Given:

The expression is:

  ${\left(9.3\times {10}^{{}^{-6}}\right)}^{-2}$

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:

  $\begin{array}{c}{\left(9.3\times {10}^{{}^{-6}}\right)}^{-2}=\frac{1}{{\left(9.3\times {10}^{{}^{-6}}\right)}^2}\\ =\frac{1}{{9.3}^2\times {\left({10}^{-6}\right)}^2}\\ =0.0116\times {10}^{12}\\ =1.16\times {10}^{10}\end{array}$

Thus, the required solution is $1.16\times {10}^{10}$ .