Question

Are you able to help again with this one? And could you explain how you came to the answer like the steps behind it?

Answer 1

Solution:

Given:

$\frac{\sqrt{16\times 10^{20}}}{4\times 10^{-4}\times 10^5}$

Splitting the numbers under the root sign as a perfect square;

$\begin{gathered} \frac{\sqrt{16\times10^{20}}}{4\times10^{-4}\times10^5}=\frac{\sqrt{4^2\times(10^{10})^2}}{4\times10^{-4}\times10^5} \\ =\frac{4\times10^{10}}{4\times10^{-4}\times10^5} \\ Cancelling\text{ out the common term;} \\ =\frac{10^{10}}{10^{-4}\times10^5} \end{gathered}$

Applying the law of exponents;

$\begin{gathered} x^a\times x^b=x^{a+b} \\ \\ Hence, \\ \frac{10^{10}}{10^{-4}\times10^5}=\frac{10^{10}}{10^{-4+5}} \\ =\frac{10^{10}}{10^1} \\ \\ Also\text{ applying the law of exponents below;} \\ \frac{x^a}{x^b}=x^{a-b} \\ \\ Hence, \\ \frac{10^{10}}{10^1}=10^{10-1} \\ =10^9 \end{gathered}$

In scientific notation, the solution is;

$1\times10^9$