Chapter 11.6, Problem 4MRE

To determine

To simplify: the given expression.

Answer to Problem 4MRE

  ${\left(3\cdot {10}^{-4}\right)}^2=0.0000000000000009$ .

Explanation of Solution

Given:

The given expression is ${\left(3\cdot {10}^{-4}\right)}^2$ .

Calculation:

As the given expression is ${\left(3\cdot {10}^{-4}\right)}^2$ .

Therefore, the given expression is expressed as,

  $\begin{array}{l}{\left(3\cdot {10}^{-4}\right)}^2={\left(\frac{3}{{10}^4}\right)}^2\left\{\because x^{-m}=\frac{1}{x^m}\right\}\\ =\left(\frac{9}{{10}^{16}}\right)\\ =0.0000000000000009\end{array}$

Thus, $\sqrt{50a^5{\left(b+4\right)}^2}=5a^2\left(b+4\right)\sqrt{2a}$

Hence, the simplified form of the given expression is ${\left(3\cdot {10}^{-4}\right)}^2=0.0000000000000009$ .