Answer:
500 times thicker.
Step-by-step explanation:
We have been given that a human hair was measured to be [tex]8.0\times10^{-4}[/tex] inch thick. A cat hair was measured to be [tex]4.0\times10^{-1}[/tex] inch thick.
To find the thickness of cat hair is how many times greater than human hair, we will divide thickness of cat hair by thickness of human hair as:
[tex]\frac{4.0\times10^{-1}}{8.0\times10^{-4}}[/tex]
Using exponent property [tex]\frac{a^m}{a^n}=a^{m-n}[/tex], we will get:
[tex]\frac{4.0\times10^{-1}}{8.0\times10^{-4}}=\frac{4.0}{8.0}\times 10^{-1-(-4)}[/tex]
[tex]\frac{4.0\times10^{-1}}{8.0\times10^{-4}}=\frac{1}{2}\times10^{-1+4}[/tex]
[tex]\frac{4.0\times10^{-1}}{8.0\times10^{-4}}=0.5\times 10^{3}[/tex]
[tex]\frac{4.0\times10^{-1}}{8.0\times10^{-4}}=0.5\times 1000[/tex]
[tex]\frac{4.0\times10^{-1}}{8.0\times10^{-4}}=500[/tex]
Therefore, the cat hair is 500 times thicker than human hair.
