A = 5 ngũ 6 trừ 5 ngũ 4 cộng 5 ngũ 2 trừ 1 [ cộng thức tính nhanh cho ví dụ này ]
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\(24\cdot5^5+5^2\cdot5^3\)
\(=24\cdot5^5+5^{2+3}\)
\(=24\cdot5^5+5^5\)
\(=5^5\cdot\left(24+1\right)\)
\(=5^5\cdot25\)
\(=5^5\cdot5^2\)
\(=5^7\)
`@` `\text {Ans}`
`\downarrow`
`24 * 5^5 + 5^2 * 5^3`
`= 24*5^5 +`\(5^{2+3}\)
`= 24*5^5 + 5^5`
`= 5^5* (24+1)`
`= 5^5*25`
`= 5^5*5^2`
`= 5^7`
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=81*(27+9^15):(3^5+3^32)
\(=\dfrac{3^4\cdot\left(3^3+3^{30}\right)}{3^5+3^{32}}=\dfrac{3^7\left(1+3^{27}\right)}{3^5\left(1+3^{27}\right)}=\dfrac{3^7}{3^5}=9\)
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a) \(5^2.3^5.\left(\frac{3}{5}\right)^2\)
\(=25.243.\frac{9}{25}\)
\(=6075.\frac{9}{25}\)
\(=2187\)
b) \(4.32.2^3.\frac{1}{16}\)
\(=4.32.8.\frac{1}{16}\)
\(=128.8.\frac{1}{16}\)
\(=1024.\frac{1}{16}\)
\(=64\)
c) \(\left(-2\frac{1}{3}\right)^2.\left(-\frac{1}{4}\right)^2\)
\(=\frac{49}{9}.\frac{1}{16}\)
\(=\frac{49}{144}\)
d) \(\frac{9^5.5^7}{45^7}\)
\(=\frac{9^5}{9^7}\)
\(=\frac{1}{9^2}=\frac{1}{81}\)
e) 103 + 5.102 + 53
= 1000 + 5.100 + 125
= 1005 . 12500
= 13505
P/s: Mũ not ngũ ^^
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:A=\(2+2^2+2^3+...+2^{60}\)
+)A=\(2.\left(1+2+2^2+...+2^{59}\right)\)
\(\Rightarrow\)\(A⋮2\)
+)A=\(\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{59}+2^{60}\right)\)
A=\(2.\left(1+2\right)+2^3.\left(1+2\right)+...+2^{59}.\left(1+2\right)\)
A=\(2.3+2^3.3+...+2^{59}.3\)
\(\Rightarrow A⋮3\)
Mà 2;3 là 2 số nguyên tố cùng nhau
\(\Rightarrow A⋮2.3\)
\(\Rightarrow A⋮6\)
Học tốt nha!!!
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