to make this sooo much easier, regroup
remember
\(\frac{ab}{cd}=( \frac{a}{c} )( \frac{b}{d} )\)
and
\(\frac{x^m}{x^n}=x^{m-n}\)
and
(ab)(cd)=(a)(b)(c)(d)=(ac)(bd)
and
\((ab)^m=(a^m)(b^m)\)
so
1.
a.
disregard the 1 exponent since it won't actally do anything
\(\frac{4*10^{-3}}{5*10^{-4}}=( \frac{4}{5} )( \frac{10^{-3}}{10^{-4}} )=( \frac{4}{5} )( \frac{10^{1}}{10^{-4}} )\)=40/5=8
b. same thing
(9/4)(10^-5/10^2)=(9/4)(10^-7)=\(2.25*10^{-7}\)
c.
notice exponent
8.8^2=17.6
10^-6^2=10^-12
(17.6/1.1)(10^-12/10^6)=1610^-18=1.610^-17
d. (8.5/2)(10^5/10^4)=4.2510^1
e.(3/2)(10^-3/10^-4)=1.510^1
2.
a.
[(8.75.7)(10^-210^6)]/(910^-5)=[(49.59)(10^4)]/(910^-5)=5.5110^9
b.
[(812)(10^510^3)]/(310^-1)^3=[(96)(10^8)]/(2710^-3)=3.5555510^11
c.
[(3.93.9)(10^-610^2)]/(910^3)=[(15.21)(10^-4)]/(910^3)=1.6910^7
d.
[(366)(10^610^1)]/(310^-7)=[(216)(10^7)]/(310^-7)= 7210^14=7.210^15
3.
a.
(9.410^8)/(5.2610^5)=(9.4/5.26)(10^8/10^5)=1.78710^3=1.7910^3km
b.
(9.410^8)/(8.7610^3)=(9.4/8.76)/(10^8/10^3)=1.07310^5=1.0710^5km
c. 45%=45/100=0.45=4.510^-1
(4.410^6)(4.510^-1)=(4.44.5)(10^610^-1)=19.810^5=$1.9610^6
