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

Given:

`\frac{\sqrt{16* 10^(20)}}{4* 10^(-4)* 10^5}`

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

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

Applying the law of exponents;

`\begin{gathered} x^a* x^b=x^(a+b) \\ \\ Hence, \\ (10^(10))/(10^(-4)*10^5)=(10^(10))/(10^(-4+5)) \\ =(10^(10))/(10^1) \\ \\ Also\text{ applying the law of exponents below;} \\ (x^a)/(x^b)=x^(a-b) \\ \\ Hence, \\ (10^(10))/(10^1)=10^(10-1) \\ =10^9 \end{gathered}`

In scientific notation, the solution is;

`1*10^9`