Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Bài 1 :
a) A = \(8^2\) . \(32^4\) = \(\)(2\(^3\))\(^2\) . ( \(2^5\))\(^4\) = 2\(^6\) . 2\(^{20}\) = 2\(^{26}\)
b) B = 27\(^3\) . 9\(^4\) . 243 = ( \(3^3\))\(^3\) . ( \(3^2\) )\(^4\) . 3\(^5\) = 3\(^9\) . \(3^8\) . 3\(^5\) = 3\(^{22}\)
Bài 2 : So sánh
a) A = 27\(^5\) và B =2433
Ta có : 27\(^5\) =(3\(^3\))\(^5\) = 3\(^8\) = 6561
Vì 6561 > 2433 nên A > B .
b) A = 2300 và B = 3\(^{200}\)
Ta có : B = \(3^{200}\) = 3\(^8\) . 3\(^{192}\) = 6561 . 3\(^{192}\)
Vậy chắc chắn rằng B > A .
\(2^{27}=2^{3\cdot9}=\left(2^3\right)^9=8^9\)
\(3^{18}=3^{2\cdot9}=\left(3^2\right)^9=9^9\)
Vậy,......
a)\(3^5.5^7.45=3^5.5^7.3^2.5=3^7.5^8\)
b)\(2^8.4^5.9^9\)\(=2^8.2^{10}.9^9=2^{18}.9^9\)
c)\(\left(2^3.3^5.5^7\right)^{10}.12^{20}=2^{13}.3^{15}.5^{17}.12^{20}\)\(=2^{13}.3^{15}.5^{17}.2^{40}.3^{20}=2^{53}.3^{35}.5^{17}\)
d)\(\left(x^2y\right)^5.\left(x^2y^2\right)^7.\left(x.y^2\right)^6.x^3=x^{10}.y^5.x^{14}.y^{14}.x^6.y^{12}.x^3\)
\(=x^{33}.y^{31}\)
e)\(18^{20}.45^5.5^{25}.8^{10}=2^{20}.3^{40}.5^5.3^{10}.5^5.5^{25}.2^{30}\)
\(=2^{50}.3^{50}.5^{35}=6^{50}.5^{35}\)
f)\(2^7.3^8.4^9.9^8=2^7.3^8.2^{18}.3^{16}=2^{25}.3^{24}\)
Bài 4:
a)Ta có: B= 23!+19!−15!
B=1.2.3.....11..23+1.2....11.19-1.2.....11.12.13.14.15
Vì 11 chia hết cho 11=>23! chia hết cho 11
19!chia hết cho 11
15! chia hết cho 11
Bài 1.
\(\frac{75}{100}+\frac{18}{21}+\frac{19}{32}+\frac{1}{4}+\frac{3}{21}+\frac{3}{32}\)
\(=\left(\frac{75}{100}+\frac{1}{4}\right)+\left(\frac{18}{21}+\frac{3}{21}\right)+\left(\frac{19}{32}+\frac{3}{32}\right)\)
\(=1+1+\frac{11}{16}\)
\(=2+\frac{11}{16}\) \(=\frac{43}{16}\)
Bài 1:
a)\(\frac{x}{5}=\frac{-12}{20}\Rightarrow20x=5.\left(-12\right)=-60\Rightarrow x=-3\)
b)\(\frac{2}{y}=\frac{11}{-66}\Rightarrow2.\left(-66\right)=11y\Rightarrow11y=-132\Rightarrow y=-12\)
c)\(\frac{-3}{6}=\frac{x}{-2}=\frac{-18}{y}=\frac{-z}{24}\)
\(\Rightarrow\left\{{}\begin{matrix}\frac{-3}{6}=\frac{x}{-2}\Rightarrow x=\frac{\left(-3\right)\left(-2\right)}{6}=1\\\frac{-3}{6}=\frac{-18}{y}\Rightarrow y=\frac{\left(-18\right).6}{-3}=36\\\frac{-3}{6}=\frac{-z}{24}\Rightarrow-z=\frac{\left(-3\right).24}{6}=-12\Rightarrow z=12\end{matrix}\right.\)
Bài 2:
\(\frac{-2}{x}=\frac{y}{3}\Rightarrow xy=\left(-2\right).3=-6\)
Mà \(x< 0< y\) nên ta có bảng sau:
| \(x\) | \(-6\) | \(-3\) | \(-2\) | \(-1\) |
| \(y\) | 1 | 2 | 3 | 6 |
a, \(2^{27}=\left(2^3\right)^9=8^9\)
\(3^{18}=\left(3^2\right)^9=9^9\)
b, Vì \(8^9< 9^9\)
Nên \(2^{27}< 3^{18}\)
a) Ta có: \(2^{27}=\left(2^3\right)^9=8^9\)
\(3^{18}=\left(3^2\right)^9=9^9\)
b) Ta có: \(2^{27}=8^9\) và \(3^{18}=9^9\)
Vì \(8< 9\Rightarrow8^9< 9^9\Rightarrow2^{27}< 3^{18}\)