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1) \(12\cdot12\cdot2\cdot12\cdot6=12\cdot12\cdot12\cdot12=12^4\)
2) \(25\cdot5\cdot4\cdot2\cdot10=\left(25\cdot4\right)\cdot\left(5\cdot2\cdot10\right)=100\cdot100=100^2=10^4\)
3) \(2\cdot10\cdot10\cdot3\cdot5\cdot10=3\cdot10\cdot10\cdot10\cdot10=3\cdot10^4\)
4) \(a\cdot a\cdot a+b\cdot b\cdot b\cdot b=a^3+b^4\)
Viết gọn các biểu thức sau bằng cách dùng lũy thừa
1) 12.12.2.12.6
=> 12 . 12 . 12 . (2 . 6)
= 12 . 12 . 12 . 12 . 12 = 125
2) 25.5.4.2.10
=> ( 25 . 4 ) . ( 2 . 5 . 10 )
= 100 . 100 = 1002
3) 2.10.10.3.5.10
=> ( 2 . 5 ) . 10 . 10 . 10 . 3
= 10 . 10 . 10 . 10 . 3 = 104 . 3
4) a.a.a cộng b.b.b.b
=> a3 + b4
`3.5 .15.15 = 3.5.3.5.3.5 = 3^3.5^3`
`2.2.5.2.5 = 2^3 . 5^2`
`1000.10 .10 = 10^3 .10^1 . 10^1 = 10^5`
`a.a.a.b.b.b = a^3 . b^3`
`n.n.n + p.p = n^3 . p^2`
a: =15*15*15=15^3
b: =2^3*5^2
c: =10^3*10^2=10^5
d: =a^3*b^3
e: =n^3+p^2
2:
a: n=5^4
=>n=625
b: n^3=125
=>n^3=5^3
=>n=5
c: 11^n=1331
=>11^n=11^3
=>n=3
`10.1000.100000`
`=10^{1}.10^{3}.10^{5}`
`=10^{1+3+5}`
`=10^{9}`
`@` `\text {Ans}`
`\downarrow`
\(7\cdot35\cdot7\cdot25\)
`=`\(7^2\cdot7\cdot5\cdot5^2\)
`=`\(7^3\cdot5^3=\left(7\cdot5\right)^3=35^3\)
a. 73
b. 7.35.7.25 = 7 . 5 . 7 . 7 . 5 . 5 = 73 . 53
c. 2.3.8.12.24 = 2.3.2.2.2.2.2.3.2.2.2.3 = 29 . 33
d. 12.12.2.12.6 = 3.2.2.3.2.2.2.3.2.2.2.3 = 34 . 29
e. 25.5.4.2.10 = 5.5.5.2.2.2.5.2 = 54 . 24
f. 2.10.10.3.5.10 = 2.2.5.2.5.3.5.2.5 = 24 . 54 . 3
g. a.a.a+b.b.b.b = a3 + b3
h. x.x.y.y.x.y.x = x4 . y3
a.\(7^3\)
b.\(7^3\cdot5^3\)
c.\(2^9\cdot3^3\)
d.\(2^8\cdot3^4\)
e.\(2^4\cdot5^4\)
f.\(2^4\cdot3\cdot5^4\)
g.\(a^3+b^4\)
h.\(x^4\cdot y^3\)
Ta có:
12 . 12 . 12 . 2. 6 = 12 . 12 . 12 . 12 = 124
25 . 5 . 4 . 2 . 10 = 25 . 4 . 2 . 10 . 5 = 100 . 100 = 1002
2. 10 . 10 . 3 . 5. 10 = 10 . 10 . 10 . 2 . 5 . 3 = 10 . 10 . 10 . 10 . 3 = 104 . 3
a,12.12.2.12.6=12.12.12.(2.6)=12.12.12.12=124
b,25.5.4.2.10=(25.4)(5.2.10)=100.100=1002
c,2.10.10.3.5.10=10.10.10.2.5.3=10.10.10.10.3=104.3