Respuesta :
We need to solve:
[tex](8.0\times10^{-5})\cdot(2.0\times10^9)[/tex]What we need to do is multiply the numbers and the powers of 10 separately. It is also very important to remember a key property of powers:
[tex]10^a\cdot10^b=10^{a+b}[/tex]Then we have:
[tex]\begin{gathered} (8.0\times10^{-5})\cdot(2.0\times10^9)=(8.0\cdot2.0)\times(10^{-5}\cdot10^9) \\ (8.0\times10^{-5})\cdot(2.0\times10^9)=16.0\times10^{-5+9}=16.0\times10^4 \end{gathered}[/tex]But we can rewrite 16.0 in scientific notation. For that purpose we can multiply it and divide it by 10:
[tex]16.0=16.0\cdot\frac{10}{10}=\frac{16.0}{10}\times10=1.6\times10[/tex]Remember that:
[tex]10=10^1[/tex]So we can write:
[tex]\begin{gathered} (8.0\times10^{-5})\cdot(2.0\times10^9)=16.0\times10^4=1.6\times10^1\cdot10^4 \\ (8.0\times10^{-5})\cdot(2.0\times10^9)=1.6\times10^{1+4}=1.6\times10^5 \end{gathered}[/tex]Then the answer is:
[tex]1.6\times10^5[/tex]