to make this sooo much easier, regroup
remember
[tex] \frac{ab}{cd}=( \frac{a}{c} )( \frac{b}{d} ) [/tex]
and
[tex] \frac{x^m}{x^n}=x^{m-n} [/tex]
and
(ab)(cd)=(a)(b)(c)(d)=(ac)(bd)
and
[tex](ab)^m=(a^m)(b^m)[/tex]
so
1.
a.
disregard the 1 exponent since it won't actally do anything
[tex] \frac{4*10^{-3}}{5*10^{-4}}=( \frac{4}{5} )( \frac{10^{-3}}{10^{-4}} )=( \frac{4}{5} )( \frac{10^{1}}{10^{-4}} ) [/tex]=40/5=8
b. same thing
(9/4)(10^-5/10^2)=(9/4)(10^-7)=[tex] 2.25*10^{-7} [/tex]
c.
notice exponent
8.8^2=17.6
10^-6^2=10^-12
(17.6/1.1)(10^-12/10^6)=16*10^-18=1.6*10^-17
d. (8.5/2)(10^5/10^4)=4.25*10^1
e.(3/2)(10^-3/10^-4)=1.5*10^1
2.
a.
[(8.7*5.7)(10^-2*10^6)]/(9*10^-5)=[(49.59)(10^4)]/(9*10^-5)=5.51*10^9
b.
[(8*12)(10^5*10^3)]/(3*10^-1)^3=[(96)(10^8)]/(27*10^-3)=3.55555*10^11
c.
[(3.9*3.9)(10^-6*10^2)]/(9*10^3)=[(15.21)(10^-4)]/(9*10^3)=1.69*10^7
d.
[(36*6)(10^6*10^1)]/(3*10^-7)=[(216)(10^7)]/(3*10^-7)= 72*10^14=7.2*10^15
3.
a.
(9.4*10^8)/(5.26*10^5)=(9.4/5.26)(10^8/10^5)=1.787*10^3=1.79*10^3km
b.
(9.4*10^8)/(8.76*10^3)=(9.4/8.76)/(10^8/10^3)=1.073*10^5=1.07*10^5km
c. 45%=45/100=0.45=4.5*10^-1
(4.4*10^6)(4.5*10^-1)=(4.4*4.5)(10^6*10^-1)=19.8*10^5=$1.96*10^6
