Question

Evaluate${(4.1\times {10}^{-4})}^2$ . Express the result in scientific notation.

Short answer

The scientific notation of the given number is $1.681\times {10}^{-7}$.

Step-by-step solution

Step 1. Write down the given expression.

The given number is ${(4.1\times {10}^{-4})}^2$.

Step 2. Expressing the given number in scientific notation.

The number ${(4.1\times {10}^{-4})}^2$ in scientific notation is expressed as:

$\begin{array}{c}{(4.1\times {10}^{-4})}^2={\left(4.1\right)}^2\times {\left({10}^{-4}\right)}^2\\ =16.81\times {10}^{-8}\\ =16.81\times {10}^{-8}\times \frac{10}{10}\left(\begin{array}{l}\text{Multiplyand}\\ \text{divideby10}\end{array}\right)\\ =1.681\times {10}^{-7}\end{array}$

Step 3. Conclusion.

The scientific notation of the given number is $1.681\times {10}^{-7}$.