Answer:
7. The numbers 14/81 are relatively prime
8. b=3
9. 0.00001
19. 11
Step-by-step explanation:
7. Relatively prime numbers have no common factors. We only have to factor each number and compare
14=2*7
35=5*7
38=2*19
81=9*9
91=7*13
The first two numbers have 7 in common
The second have 2 in common
The third set have no common factors
The fourth set have 7 in common
The numbers 14/81 are relatively prime
8. ![b^{-3}=\frac{1}{27} => b^3=27 => b=\sqrt[3]{27} =3](https://tex.z-dn.net/?f=b%5E%7B-3%7D%3D%5Cfrac%7B1%7D%7B27%7D%20%3D%3E%20b%5E3%3D27%20%3D%3E%20b%3D%5Csqrt%5B3%5D%7B27%7D%20%3D3)
9. ![10^{-5}=\frac{1}{100000}=0.00001](https://tex.z-dn.net/?f=10%5E%7B-5%7D%3D%5Cfrac%7B1%7D%7B100000%7D%3D0.00001)
10. 100,000,000,000=10*10*...10 as many times as zeroes there are, so
![100,000,000,000=10^{11}](https://tex.z-dn.net/?f=100%2C000%2C000%2C000%3D10%5E%7B11%7D)