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b: \(7\cdot2^{13}< 8\cdot2^{13}=2^{16}\)
d: \(3^{99}=\left(3^{33}\right)^3\)
\(11^{21}=\left(11^7\right)^3\)
mà \(3^{33}>11^7\)
nên \(3^{99}>11^{21}\)
b)
\(4\frac{5}{9}:2\frac{5}{18}-7< x< \left(3\frac{1}{5}:3,2+4,5.1\frac{31}{45}\right):\left(21.\frac{1}{2}\right)\)
\(\Rightarrow\frac{41}{9}:\frac{41}{18}-7< x< \left(\frac{16}{5}:\frac{16}{5}+\frac{9}{2}.\frac{76}{45}\right):\frac{21}{2}\)
\(\Rightarrow2-7< x< \left(1+\frac{38}{5}\right):\frac{21}{2}\)
\(\Rightarrow-5< x< \frac{43}{5}:\frac{21}{2}\)
\(\Rightarrow-5< x< \frac{86}{105}\)
Vì \(x\in Z\left(gt\right)\)
\(\Rightarrow x\in\left\{-4;-3;-2;-1;0\right\}.\)
Vậy \(x\in\left\{-4;-3;-2;-1;0\right\}.\)
1.
\(a.\frac{1}{2}+a.\frac{1}{4}=-\frac{4}{5}\Rightarrow a.\left(\frac{1}{2}+\frac{1}{4}\right)=-\frac{4}{5}\Rightarrow a=-\frac{16}{15}\)
2. Ta có:
\(A=\left(2\frac{5}{6}+1\frac{4}{9}\right):\left(10\frac{1}{12}-9\frac{1}{2}\right)=\left(\frac{17}{6}+\frac{13}{9}\right):\left(\frac{121}{12}-\frac{19}{2}\right)=\frac{77}{18}:\frac{7}{12}=\frac{22}{3}\)
\(B=1\frac{5}{18}-\frac{5}{18}\left(\frac{1}{15}+1\frac{1}{3}\right)=\frac{23}{18}-\frac{5}{18}\left(\frac{1}{15}+\frac{4}{3}\right)=\frac{23}{18}-\frac{1}{54}-\frac{10}{27}=\frac{8}{9}\)
Có: \(\frac{22}{3}=\frac{66}{9}>\frac{8}{9}\Leftrightarrow A>B\)
a) Đặt \(A=\frac{7^{15}}{1+7+7^2+...+7^{14}}\)
Đặt \(B=1+7+7^2+...+7^{14}\)
\(\Rightarrow7B=7+7^2+...+7^{15}\)
\(\Rightarrow7B-B=6B=7^{15}-1\)
\(\Rightarrow B=\frac{7^{15}-1}{6}\)
\(\Rightarrow A=\frac{7^{15}-1+1}{\frac{7^{15}-1}{6}}=\left(7^{15}-1\right).\frac{6}{7^{15}-1}+\frac{6}{7^{15}-1}=6+\frac{6}{7^{15}-1}\)
Tự làm tiếp nha
A. \(\frac{3}{4}\) x \(\frac{8}{9}\)x \(\frac{15}{16}\)x .... x \(\frac{899}{900}\)
= \(\frac{1.3}{2^2}\) x \(\frac{2.4}{3^3}\)x \(\frac{3.5}{4^2}\)x ... x \(\frac{29.31}{30^2}\)
= \(\left(\frac{1.2.3...29}{2.3.4...30}\right).\left(\frac{3.4.5...31}{2.3.4...30}\right)\)
= \(\frac{1}{30}.\frac{31}{2}\)= \(\frac{31}{60}\)
B.
\(\frac{1}{3}+\frac{3}{8}-\frac{7}{12}=\frac{8}{24}+\frac{9}{24}-\frac{14}{24}=\frac{8+9-14}{24}=\frac{3}{24}=\frac{1}{8}\)
A = 8 15 . 21 12 , B = ( − 3 ) 5 . ( − 7 ) 9 ; A = 8 15 . 21 12 = 8.21 15.12 = 4.2.3.7 3.5.4.3 = 14 15 B = ( − 3 ) 5 . ( − 7 ) 9 = ( − 3 ) . ( − 7 ) 5.9 = 3.7 5.3.3 = 7 15 V ì 14 15 > 7 15 n ê n A > B