Viết kết quả của các phép tính sau dưới dạng lũy thừa:
a) 34.273.815 b) 105.100.10003 c) 256:25:
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![](https://rs.olm.vn/images/avt/0.png?1311)
a) \({2^m}{.2^n}=\underbrace {2.2 \ldots .2}_{m{\rm{ }}}{\rm{ }}.\underbrace {2.2 \ldots .2}_{n{\rm{ }}}{\rm{ }}\) = 2m+n
b) \({3^m}:{3^n}=(\underbrace {3.3 \ldots .3}_{m{\rm{ }}}{\rm{ }}):(\underbrace {3.3 \ldots .3}_{n{\rm{ }}}{\rm{ }})\) = 3m-n với \(m \ge n\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a. \(3^4.3^5=3^9\)
\(16.2^9=2^4.2^9=2^{13}\)
\(16.32=2^4.2^5=2^9\)
b. \(12^8.12=12^9\)
\(243:3^4=3^5:3^4=3\)
\(10^9:10000=10^9:10^4=10^5\)
c. \(4.8^6.2.8^3=2^2.2^{18}.2.2^9=2^{30}\)
\(12^2.2.12^3.6=12^2.12.12^3=12^6\)
\(6^3.2.6^4.3=6^3.6.6^4=6^8\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\frac{6}{5}.{\left( {1,2} \right)^8} = 1,2.{(1,2)^8} = {(1,2)^{1 + 8}} = {(1,2)^9}\)
b) \({\left( {\frac{{ - 4}}{9}} \right)^7}:\frac{{16}}{{81}} = {\left( {\frac{{ - 4}}{9}} \right)^7}:{\left( {\frac{{ - 4}}{9}} \right)^2} = {\left( {\frac{{ - 4}}{9}} \right)^{7 - 2}} = {\left( {\frac{{ - 4}}{9}} \right)^5}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) `7^4 .7^5 .7^6 = 7^(4+5+6)=7^(15)`
b) `(54:3^7) .324 =( 2.3^3 : 3^7).2^2 x3^4`
`=(2: 3^4).3^4 .2^2`
`= 2.2^2=2^3`
c) `[(8+2^2).10^100] : (10^0 .10^94)`
`=(12 . 10^100) : 10^94`
`=12 . (10^100 : 10^94)`
`=12 . 10^6`
d) `a^9 :a^9 = a^(9-9)=a^0`
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(3^3 : 3^2\)=\(3^{3-2}=3^1\)
b) \(5^{4} : 5^{2}\)=\(5^{4-2}=5^2\)
c) \(8^{3} . 8^{2}\)=\(8^{3+2}=8^5\)
d) Cách 1:
\(5^{4} . 5^{3}: 5^{2}=5^{4+3}:5^2=5^7:5^2=5^{7-2}=5^5\)
Cách 2:
\(5^{4} . 5^{3}: 5^{2}=5^{4+3-2}=5^5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(25^2:100^0=\left(5^2\right)^2:1=5^4\\ 30^3:30^0=2^3.3^3.5^3:1=2^3.3^3.5^3\)
Đáp án :
a.34 . 273 . 815
= 34 . ( 3 )3.3 . ( 3 )4.15
= 34 . 39 . 360
= 34+9+60
= 373
b.105 . 100 . 10003
= 105 . 102 . ( 10 )100.3
= 105 . 102 . 10300
= 105+2+300
= 10307
c. 256 : 25
= 28 : 25
= 28-5
= 23 = 8