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a, 273 : 35 = ( 33)3 : 35 = 39 : 35 = 34
b, 72 . 343 . 4930 = 72. 73.(72)3 = 711
c, 625 : 53 = 54 : 53 = 5
d, 1 000 000 : 103 = 106 . 103 = 103
e, 115 : 121= 115 : 112 = 113
f, 87 : 64 :8 = 87 : 82 : 81 = 84
i, 1024 . 16 : 26 = 210 . 23 : 26 = 27
1) a) 4⁸.2²⁰ = (2²)⁸.2²⁰
= 2¹⁶.2²⁰ = 2³⁶
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9¹².27⁵.81³ = (3²)¹².(3³)⁵.(3⁴)⁴
= 3²⁴.3¹⁵.3¹⁶ = 3⁵⁵
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64³.4⁵.16² = (4³)³.4⁵.(4²)²
= 4⁹.4⁵.4⁴ = 4¹⁸
b) 25²⁰.125⁴ = (5²)²⁰.(5³)⁴
= 5⁴⁰.5¹² = 5⁵²
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x⁷.x³.x⁴ = x¹⁴
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3⁶.4⁶ = (3.4)⁶ = 12⁶
2) a) 2² = 4
2³ = 8
2⁴ = 16
2⁵ = 32
2⁶ = 64
2⁷ = 128
2⁸ = 256
2⁹ = 512
2¹⁰ = 1024
b) 3² = 9
3³ = 27
3⁴ = 81
3⁵ = 243
c) 4² = 16
4³ = 64
4⁴ = 256
d) 5² = 25
5³ = 125
5⁴ = 625
a) \(2^5.8^4=2^5.\left(2^3\right)^4=2^5.2^{12}=2^{5+12}=5^{17}\)
b) \(25^6.125^3=\left(5^2\right)^6.\left(5^3\right)^3=5^{12}.5^9=5^{12+9}=5^{21}\)
c) \(625^5:25^7=\left(5^4\right)^7:\left(5^2\right)^7=5^{28}:5^{14}=5^{28-14}=5^{14}\)
d) \(12^3.3^3=\left(12.3\right)^3=36^3\)
Dấu chấm là nhân nhé
minh anh sai rồi câu a là 2 mũ 17 mà ghi là 5 mũ 17
\(\dfrac{3}{2}\times\dfrac{9}{4}\times\dfrac{81}{16}=\dfrac{3}{2}\times\left(\dfrac{3}{2}\right)^2\times\left(\dfrac{3}{2}\right)^4=\left(\dfrac{3}{2}\right)^7\)
\(\left(\dfrac{1}{2}\right)^7\times8\times32\times2^8=\left(\dfrac{1}{2}\right)^7\times2^3\times2^5\times2^8=\left(\dfrac{1}{7}\right)^7\times2^{16}\)
\(\left(-\dfrac{1}{7}\right)^4\times125\times5=\left(-\dfrac{1}{7}\right)^4\times5^3\times5=\left(-\dfrac{1}{7}\right)^4\times5^4\)
\(4\times32:\left(2^3\times\dfrac{1}{16}\right)=2^2\times2^5:2^3:2^{-4}=2^0\)
\(\left(\dfrac{1}{7}\right)^2\times\dfrac{1}{7}\times49=\left(\dfrac{1}{7}\right)^3\times7^3=1^3\)
6, \(\dfrac{3}{2}\times\dfrac{9}{4}\times\dfrac{81}{16}=\dfrac{3}{2}\times\left(\dfrac{3}{2}\right)^2\times\left(\dfrac{3}{2}\right)^4\)
7,\(\left(\dfrac{1}{2}\right)^7\times8\times32\times2^8=\left(\dfrac{1}{2}\right)^7\times2^3\times2^5\times2^8\)
8,\(\left(-\dfrac{1}{7}\right) ^4\times125\times5=\left(\dfrac{1}{7}\right)^4\times5^3\times5\)
9,\(4\times32:\left(2^3\times\dfrac{1}{16}\right)=2^2\times2^5:\left[2^3\times\left(\dfrac{1}{2}\right)^4\right]\)
10, \(\left(\dfrac{1}{7}\right)^2\times\dfrac{1}{7}\times49=\left(\dfrac{1}{7}\right)^2\times\dfrac{1}{7}\times7^2\)
a: \(2^6\cdot3^3=\left(2^2\cdot3\right)^3=12^3\)
b: \(6^4\cdot8^3=2^4\cdot3^4\cdot2^9=2^{13}\cdot3^4\)
c: \(16\cdot81=36^2\)
d: \(25^4\cdot2^8=100^4\)
a, 48.84
= (22)8.(23)4
= 216.212
= 228
b, 415.515
= (4.5)15
= 2015
c, 210.15 + 210.85
= 210.(15 + 85)
= 210.100
=210.(2.5)2
= 212.52
d, 33.92
= 33 . (32)2
= 33.34
= 37
e, 512.7 - 511.10
= 511.(5.7 - 10)
= 511.25
=511.52
=513
f, \(x^1\).\(x^2\).\(x^3\)....\(x^{100}\)
= \(x^{1+2+3+...+100}\)
= \(x^{\left(1+100\right).100:2}\)
= \(x^{5050}\)
a; 25 x 53 x \(\dfrac{1}{625}\) x 52
= 52 x 53 x \(\dfrac{1}{5^4}\) x 52
= 55 x \(\dfrac{1}{5^4}\) x 52
= 5 x 52
= 53
a)
\(25\cdot5^3\cdot\dfrac{1}{625}\cdot5^2\\ =\left(5^2\cdot5^3\cdot5^2\right)\cdot\dfrac{1}{625}\\ =5^7\cdot\dfrac{1}{5^4}\\ =5^3\)
b)
\(5^2\cdot3^5\cdot\left(\dfrac{3}{5}\right)^2\\ =5^2\cdot3^5\cdot\dfrac{3^2}{5^2}\\ =3^5\cdot3^2\\ =3^7\)
c)
\(\left(-\dfrac{1}{7}\right)^4\cdot49^2\\ =\dfrac{\left(-1\right)^4}{7^4}\cdot\left(7^2\right)^2\\ =\dfrac{1}{7^4}\cdot7^4\\ =1\)
d)
\(\left(\dfrac{1}{16}\right)^2:\left(\dfrac{1}{2}\right)^4\cdot\left(-\dfrac{1}{8}\right)^3\\ =\left[\left(\dfrac{1}{2}\right)^4\right]^2:\left(\dfrac{1}{2}\right)^4\cdot\left[\left(-\dfrac{1}{2}\right)^3\right]^3\\ =\left(\dfrac{1}{2}\right)^8:\left(\dfrac{1}{2}\right)^4\cdot\left(-\dfrac{1}{2}\right)^9\\ =\left(\dfrac{1}{2}\right)^4\cdot\left(-\dfrac{1}{2}\right)^9\\ =\left(\dfrac{1}{2}\right)^4\cdot-\left(\dfrac{1}{2}\right)^9\\ =-\left(\dfrac{1}{2}\right)^{13}\)