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8=2^3 ; 20=20^1 ; 60=60^1 ; 90=90^1
16=2^4 ; 27=3^3 ; 81=3^4 ; 100=10^2
1.
a) \(3^4\times3^5\times3^6=3^{4+5+6}=3^{15}\)
b) \(5^2\times5^4\times5^5\times25=5^2\times5^4\times5^5\times5^2=5^{2+4+5+2}=5^{13}\)
c) \(10^8\div10^3=10^{8-3}=10^5\)
d) \(a^7\div a^2=a^{7-2}=a^5\)
2.
\(987=900+80+7\\ =9\times100+8\times10+7\\ =9\times10^2+8\times10^1+7\times10^0\)
\(2021=2000+20+1\\ =2\times1000+2\times10+1\times1\\ =2\times10^3+2\times10^1+1\times10^0\)
\(abcde=a\times10000+b\times1000+c\times100+d\times10+e\times1\\ =a\times10^4+b\times10^3+c\times10^2+d\times10^1+e\times10^0\)
a) 53 . 52 . 5
= 55 . 5
= 55 . 51
= 56
b) 69 : 64
= 65
c) 4 . 8 . 16 . 32
= 22 . 23 . 24 . 25
= 25 . 24 . 25
= 29 . 25
= 214
\(\begin{array}{l}a){15^8}{.2^4} = {15^{2.4}}{.2^4} = {({15^2})^4}{.2^4}\\ = {225^4}{.2^4} = {(225.2)^4} = {450^4}\\b){27^5}:{32^3} = {({3^3})^5}:{({2^5})^3}\\ = {3^{3.5}}:{2^{5.3}} = {3^{15}}:{2^{15}} = {\left( {\frac{3}{2}} \right)^{15}}\end{array}\)
a) \(15^8\cdot2^4=3^8\cdot5^8\cdot2^4=9^4\cdot25^4\cdot2^4=\left(9\cdot25\cdot2\right)^4=450^4\)
b) \(27^5:32^3=\left(3^3\right)^5:\left(2^5\right)^3=3^{15}:2^{15}=\left(\dfrac{3}{2}\right)^{15}\)
b: \(3^4\cdot3^5:\dfrac{1}{27}==3^9\cdot3^3=3^{12}\)
Đáp án B
Ta có: P = a 2 + 5 2 + 4 3 a 5 6 = a 35 6 a 5 6 = a 5