The expression [tex]\frac{(8 * 10^{2} )* (3.2 * 10^{5} )}{4 * 10^{3} }[/tex] in scientific notation written as [tex]6.4 * 10^{1}[/tex].
What is scientific notation?
It is the way of writing very small and very large numbers in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent .
Its basic rule is that while writing a number under scientific notation rule then its absolute value of the coefficient equal or greater then 1 but less then 10.
Given that:
[tex]\frac{(8 * 10^{2} )* (3.2 * 10^{5} )}{4 * 10^{3} }[/tex]
Make all exponent powers 5 for the base 10:
[tex]\frac{(0.008 * 10^{5} )* (3.2 * 10^{5} )}{0.04 * 10^{5} }[/tex]
Take [tex]10^{5}[/tex] common and eliminate:
[tex]\frac{(0.008 )* (3.2 )}{0.04}[/tex]
Now evaluate:
[tex]\frac{(0.008 )* (3.2 )}{0.04}[/tex] = 0.64
Under scientific notation rule, 0.64 written as:
6.4 x [tex]10^{1}[/tex]
Hence the value of the expression in scientific notation is 6.4 x [tex]10^{1}[/tex].
To learn more about scientific notation, refer to the link:
https://brainly.com/question/18073768
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