Respuesta :
The true statement that compares both expressions is [tex]\frac{3.56 \times 10^2}{1.09 \times 10^4} > (4.08 \times 10^2 ) \cdot (1.95 \times 10^{-6})[/tex]
The expressions on either side are given as:
[tex]\frac{3.56 \times 10^2}{1.09 \times 10^4}[/tex]
[tex](4.08 \times 10^2 ) \cdot (1.95 \times 10^{-6})[/tex]
Start by simplifying both expressions, and then make comparison.
For the first expression, we have:
[tex]\frac{3.56 \times 10^2}{1.09 \times 10^4}[/tex]
Split
[tex]\frac{3.56 \times 10^2}{1.09 \times 10^4} = \frac{3.56}{1.09} \times \frac{10^2}{10^4}[/tex]
Apply law of indices
[tex]\frac{3.56 \times 10^2}{1.09 \times 10^4} = \frac{3.56}{1.09} \times 10^{2-4}[/tex]
[tex]\frac{3.56 \times 10^2}{1.09 \times 10^4} = \frac{3.56}{1.09} \times 10^{-2[/tex]
Divide 3.56 by 1.09
[tex]\frac{3.56 \times 10^2}{1.09 \times 10^4} = 3.27 \times 10^{-2[/tex]
For the second expression, we have:
[tex](4.08 \times 10^2 ) \cdot (1.95 \times 10^{-6})[/tex]
Expand as follows:
[tex](4.08 \times 10^2 ) \cdot (1.95 \times 10^{-6}) = (4.08 \times 1.95) \cdot ( 10^2 \times 10^{-6})[/tex]
Apply law of indices
[tex](4.08 \times 10^2 ) \cdot (1.95 \times 10^{-6}) = (4.08 \times 1.95) \cdot ( 10^{2-6})[/tex]
[tex](4.08 \times 10^2 ) \cdot (1.95 \times 10^{-6}) = (4.08 \times 1.95) \cdot ( 10^{-4})[/tex]
Multiply 4.08 and 1.95
[tex](4.08 \times 10^2 ) \cdot (1.95 \times 10^{-6}) = 7.96 \times 10^{-4}[/tex]
[tex]\frac{3.56 \times 10^2}{1.09 \times 10^4}[/tex] and [tex](4.08 \times 10^2 ) \cdot (1.95 \times 10^{-6})[/tex] becomes
[tex]3.27 \times 10^{-2} \ [\ \ ] 7.96 \times 10^{-4}[/tex]
By comparison, the expression on the left-hand side is greater than the expression in the right-hand side
So, we have:
[tex]3.27 \times 10^{-2} \ > 7.96 \times 10^{-4}[/tex]
So, the true statement is
[tex]\frac{3.56 \times 10^2}{1.09 \times 10^4} > (4.08 \times 10^2 ) \cdot (1.95 \times 10^{-6})[/tex]
Read more about inequalities at:
https://brainly.com/question/18881247
