Chapter 7.3, Problem 1STP

Solve each exercise and enter your answer on the grid provided.

What is the simplified form of ${\left(2\times {10}^2\right)}^2$ in standard notation?

To determine

To find: The scientific notation of the provided expression.

Answer to Problem 1STP

The scientific notation is $4\times {10}^4$

Explanation of Solution

Given:

The expression is:

  ${\left(2\times {10}^2\right)}^2$

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:

  $\begin{array}{c}{\left(2\times {10}^2\right)}^2=2^2\times {10}^4\\ =4\times {10}^4\end{array}$

Thus, the required solution is $4\times {10}^4$ .