Question

One terameter equals 12 10 meters. One micrometer equals 6 10 − meter. One nanometer equals 9 10 −meter. A. Find the product of one terameter and one micrometer, using only positive exponents. B. Find the quotient of one terameter and one micrometer, using only positive exponents. C. Find the product of one terameter and one nanometer, using only positive exponents. D. Find the quotient of one terameter and one nanometer, using only positive exponents. E. Find the quotient of one nanometer and one terameter, using only positive exponents. F. Find the quotient of one nanometer and one micrometer, using only positive exponents. G. Find the product of one nanometer and one micrometer, using only positive exponents.

Answer 1

a)
`x = 10^(18)\,\mu m^(2)`, b)
`x = 10^(18)`, c)
`x = 10^(21)\,\mu m^(2)`, d)
`x = 10^(21)`, e)
`x = (1)/(10^(21))`, f)
`x = 10^(3)\,nm^(2)`, g)
`x = 10^(3)\,nm^(2)`

Explanation:

a) The product of one terameter and one micrometer is:

`x = (1\,tm)\cdot (10^(12)\,(m)/(tm))\cdot (10^(6)\,(\mu m)/(m) ) \cdot (1\,\mu m)`

`x = (10^(18)\,\mu m)\cdot (1\,\mu m)`

`x = 10^(18)\,\mu m^(2)`

b) The quotient of one terameter and one micrometer is:

`x = ((1\,tm)\cdot (10^(12)\,(m)/(tm) )\cdot (10^(6)\,(\mu m)/(m) ))/(1\,\mu m)`

`x = (10^(18)\,\mu m)/(1\,\mu m)`

`x = 10^(18)`

c) The product of terameter and one nanometer is:

`x = (1\,tm)\cdot (10^(12)\,(m)/(tm))\cdot (10^(9)\,(nm)/(m) ) \cdot (1\,nm)`

`x = (10^(21)\,nm)\cdot (1\,nm)`

`x = 10^(21)\,\mu m^(2)`

d) The quotient of one terameter and one nanometer is:

`x = ((1\,tm)\cdot (10^(12)\,(m)/(tm) )\cdot (10^(9)\,(nm)/(m) ))/(1\,nm)`

`x = (10^(21)\,nm)/(1\,nm)`

`x = 10^(21)`

e) The quotient of one nanometer and one terameter is:

`x = (1\,nm)/((1\,tm)\cdot (10^(12)\,(m)/(tm) )\cdot (10^(9)\,(nm)/(m) ))`

`x = (1\,nm)/(10^(21)\,nm)`

`x = (1)/(10^(21))`

f) The quotient of one nanometer and one micrometer is:

`x = (1\,nm)/((1\,\mu m)\cdot (10^(3)\,(nm)/(\mu m) ))`

`x = (1\,nm)/(10^(3)\,nm)`

`x = (1)/(10^(3))`

g) The product of one nanometer and one micrometer is:

`x = (1\,nm)\cdot (1\,\mu m)\cdot (10^(3)\,(nm)/(\mu m) )`

`x = 10^(3)\,nm^(2)`