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[tex]\displaystyle\\(5.2\cdot10^{-6})\times(8\cdot10^3)=\\\\=\underbrace{5.2\times8}_{41.6}\times\underbrace{10^{-6}\times10^{3}}_{10^{-6+3}}=\\\\=41.6\times10^{-6+3}=\boxed{\bf41.6\times10^{-3}}\\\\\texttt{Correct answer:}~~\boxed{\bf C)}[/tex]



JeanaShupp

Answer: B) [tex]4.16\cdot10^{-2}[/tex]

Step-by-step explanation:

The given product : [tex](5.2\cdot10^{-6})\cdot (8\cdot10^3)[/tex]

First open parenthesis :

[tex]5.2\cdot10^{-6}\cdot 8\cdot10^3[/tex]

Write decimal values together and power of 10s together.

[tex]5.2\cdot 8\cdot10^{-6}\cdot10^3[/tex]

Using Law of exponent : [tex]a^m\cdot a^n= a^{m+n}[/tex]

The above expression becomes.

[tex]41.6\cdot10^{-6+3}=41.6\times10^{-3}[/tex]

In scientific notation, the decimal must be placed after one digit (from left).

[tex]41.6\times10^{-3}=4.16\times10\times10^{-3}\\\\=4.16\cdot10^{-3+1}\\\\=4.16\cdot10^{-2}[/tex]

Hence, the correct answer is B) [tex]4.16\cdot10^{-2}[/tex] .

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