Here we need to compare the orders of magnitude of two measures.
We will see that the bacteria is 300 times larger than the virus.
We know that:
The diameter of the virus-cell is:
[tex]D_v = 3 \cdot 10^{-9} m[/tex]
The diameter of the bacteria cell is:
[tex]D_b = 9 \cdot 10^{-7} m[/tex]
So, to compare them, first notice that both are in the same units, meters, so we only need to compare the numbers.
Is common sense to identify the one with the largest exponent as the largest number, and the largest exponent is -7, thus the bacteria should be the larger one.
But let's prove this with math, remember the property:
[tex]\frac{a^n}{a^m} = a^{n - m}[/tex]
Let's take the quotient between the diameters and see what we get, I will use the diameter of the bacteria in the numerator, thus if the quotient is larger than 1, it would mean that the bacteria is greater and by how much.
[tex]quotient = \frac{ 9 \cdot 10^{-7} m}{ 3 \cdot 10^{-9} m} = \frac{9}{3} \cdot 10^{-7 + 9}\\\\= 3*10^2[/tex]
So we can say that the bacteria is 3*10^2 = 3*100 = 300 times larger than the virus.
If you want to learn more, you can read:
https://brainly.com/question/4953281
