Answer:
a) [tex]x = 10^{18}\,\mu m^{2}[/tex], b) [tex]x = 10^{18}[/tex], c) [tex]x = 10^{21}\,\mu m^{2}[/tex], d) [tex]x = 10^{21}[/tex], e) [tex]x = \frac{1}{10^{21}}[/tex], f) [tex]x = 10^{3}\,nm^{2}[/tex], g) [tex]x = 10^{3}\,nm^{2}[/tex]
Step-by-step explanation:
a) The product of one terameter and one micrometer is:
[tex]x = (1\,tm)\cdot (10^{12}\,\frac{m}{tm})\cdot (10^{6}\,\frac{\mu m}{m} ) \cdot (1\,\mu m)[/tex]
[tex]x = (10^{18}\,\mu m)\cdot (1\,\mu m)[/tex]
[tex]x = 10^{18}\,\mu m^{2}[/tex]
b) The quotient of one terameter and one micrometer is:
[tex]x = \frac{(1\,tm)\cdot (10^{12}\,\frac{m}{tm} )\cdot (10^{6}\,\frac{\mu m}{m} )}{1\,\mu m}[/tex]
[tex]x = \frac{10^{18}\,\mu m}{1\,\mu m}[/tex]
[tex]x = 10^{18}[/tex]
c) The product of terameter and one nanometer is:
[tex]x = (1\,tm)\cdot (10^{12}\,\frac{m}{tm})\cdot (10^{9}\,\frac{nm}{m} ) \cdot (1\,nm)[/tex]
[tex]x = (10^{21}\,nm)\cdot (1\,nm)[/tex]
[tex]x = 10^{21}\,\mu m^{2}[/tex]
d) The quotient of one terameter and one nanometer is:
[tex]x = \frac{(1\,tm)\cdot (10^{12}\,\frac{m}{tm} )\cdot (10^{9}\,\frac{nm}{m} )}{1\,nm}[/tex]
[tex]x = \frac{10^{21}\,nm}{1\,nm}[/tex]
[tex]x = 10^{21}[/tex]
e) The quotient of one nanometer and one terameter is:
[tex]x = \frac{1\,nm}{(1\,tm)\cdot (10^{12}\,\frac{m}{tm} )\cdot (10^{9}\,\frac{nm}{m} )}[/tex]
[tex]x = \frac{1\,nm}{10^{21}\,nm}[/tex]
[tex]x = \frac{1}{10^{21}}[/tex]
f) The quotient of one nanometer and one micrometer is:
[tex]x = \frac{1\,nm}{(1\,\mu m)\cdot (10^{3}\,\frac{nm}{\mu m} )}[/tex]
[tex]x = \frac{1\,nm}{10^{3}\,nm}[/tex]
[tex]x = \frac{1}{10^{3}}[/tex]
g) The product of one nanometer and one micrometer is:
[tex]x = (1\,nm)\cdot (1\,\mu m)\cdot (10^{3}\,\frac{nm}{\mu m} )[/tex]
[tex]x = 10^{3}\,nm^{2}[/tex]
