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\(27^5\cdot32^3=\left(3^3\right)^5\cdot\left(2^5\right)^3=3^{15}\cdot2^{15}=\left(2\cdot3\right)^{15}=6^{15}\)
Ko biết đề có phải thế này ko, bạn viết khó hiểu quá ??
\(3^2\cdot\left(3^3\right)^n=3^8\)
\(3^{3n}=3^6\)
=> 3n = 6
=> n = 2
\(\frac{1}{2}.2^n+2^{2+n}=9.2^5\)
\(\frac{1}{2}.2^n+4.2^n=9.2^5\)
\(2^n.\left(\frac{1}{2}+4\right)=9.2^5\)
\(2^n.\frac{9}{2}=9.2^5\)
\(2^n=9.\frac{2}{9}.2^5\)
\(2^n=2.2^5\)
\(2^n=2^6\)
\(\Rightarrow n=6\)
\(\frac{1}{2}\)\(\times\)\(2^n\)\(+\)\(2^{2+n}\)\(=\)\(9\)\(\times\)\(2^5\)
\(\frac{1}{2}\)\(\times\)\(2^n\)\(\times\)\((\)\(1\)\(+\)\(2^2\)\()\)\(=\)\(9\)\(\times\)\(2^5\)
\(\frac{1}{2}\)\(\times\)\(2^n\)\(\times\)\(5\)\(=\)\(9\)\(\times\)\(2^5\)
\(2^n\)\(=\)\(9\)\(\times\)\(32\)\(\div\)\(5\)\(\times\)\(2\)
\(2^n\)\(=\)115,2
\(2^9\cdot\dfrac{81}{3^5\cdot8^2}=\dfrac{2^9\cdot3^4}{3^5\cdot2^6}=2^3\cdot\dfrac{1}{3}=\dfrac{8}{3}\)
Có: 7-3.\(\frac{-1}{4}^2\)
= 7-3. \(\frac{1}{16}\)
= 7- \(\frac{3}{16}\)
= \(\frac{112}{16}\)-\(\frac{3}{16}\)
= \(\frac{109}{16}\)
a) \(12\cdot\left(-\dfrac{2}{3}\right)^2+\dfrac{4}{3}\)
\(=12\cdot\dfrac{4}{9}+\dfrac{4}{3}\)
\(=\dfrac{12\cdot4}{9}+\dfrac{4}{3}\)
\(=\dfrac{16}{3}+\dfrac{4}{3}\)
\(=\dfrac{16+4}{3}\)
\(=\dfrac{20}{3}\)
b) \(\left(\dfrac{3}{2}\right)^2-\left[0,5:2-\sqrt{81}\cdot\left(-\dfrac{1}{2}\right)^2\right]\)
\(=\dfrac{9}{4}-\left(\dfrac{1}{2}:2-9\cdot\dfrac{1}{4}\right)\)
\(=\dfrac{9}{4}-\left(\dfrac{1}{4}-9\cdot\dfrac{1}{4}\right)\)
\(=\dfrac{9}{4}-\dfrac{1}{4}\cdot\left(1-9\right)\)
\(=\dfrac{9}{4}+\dfrac{8}{4}\)
\(=\dfrac{17}{4}\)
c) \(\left(-\dfrac{3}{4}+\dfrac{2}{3}\right):\dfrac{5}{11}+\left(-\dfrac{1}{4}+\dfrac{1}{3}\right)\)
\(=-\dfrac{1}{12}:\dfrac{5}{11}+\dfrac{1}{12}\)
\(=\dfrac{1}{12}\cdot-\dfrac{11}{5}+\dfrac{1}{12}\)
\(=\dfrac{1}{12}\cdot\left(-\dfrac{11}{5}+1\right)\)
\(=\dfrac{1}{12}\cdot-\dfrac{6}{5}\)
\(=-\dfrac{1}{10}\)
d) \(\dfrac{\left(-1\right)^3}{15}+\left(-\dfrac{2}{3}\right)^2:2\dfrac{2}{3}-\left|-\dfrac{5}{6}\right|\)
\(=-\dfrac{1}{15}+\dfrac{4}{9}:\left(2+\dfrac{2}{3}\right)-\dfrac{5}{6}\)
\(=-\dfrac{1}{15}+\dfrac{4}{9}:\dfrac{8}{3}-\dfrac{5}{6}\)
\(=-\dfrac{9}{10}+\dfrac{1}{6}\)
\(=-\dfrac{11}{15}\)
e) \(\dfrac{3^7\cdot8^6}{6^6\cdot\left(-2\right)^{12}}\)
\(=\dfrac{3^7\cdot\left(2^3\right)^6}{2^6\cdot3^6\cdot2^{12}}\)
\(=\dfrac{3^7\cdot2^{18}}{2^{6+12}\cdot3^6}\)
\(=\dfrac{2^{18}\cdot3^7}{2^{18}\cdot3^6}\)
\(=3^{7-6}\)
\(=3\)
\(a,12\cdot\left(-\dfrac{2}{3}\right)^2+\dfrac{4}{3}\\ =12\cdot\dfrac{4}{9}+\dfrac{4}{3}\\ =\dfrac{16}{3}+\dfrac{4}{3}\\ =\dfrac{20}{3}\\ b,\left(\dfrac{3}{2}\right)^2-\left[0,5:2-\sqrt{81}.\left(-\dfrac{1}{2}\right)^2\right]\\ =\dfrac{9}{4}-\left(\dfrac{1}{2}\cdot\dfrac{1}{2}-9\cdot\dfrac{1}{4}\right)\\ =\dfrac{9}{4}-\left(\dfrac{1}{4}-\dfrac{9}{4}\right)\\ =\dfrac{9}{4}-\left(-\dfrac{8}{4}\right)\\ =\dfrac{17}{4}\)
\(c,\left(-\dfrac{3}{4}+\dfrac{2}{3}\right):\dfrac{5}{11}+\left(-\dfrac{1}{4}+\dfrac{1}{3}\right)\\ =\left(-\dfrac{9}{12}+\dfrac{8}{12}\right)\cdot\dfrac{11}{5}+\left(-\dfrac{3}{12}+\dfrac{4}{12}\right)\\ =-\dfrac{1}{12}\cdot\dfrac{11}{5}+\dfrac{1}{12}\\ =-\dfrac{11}{60}+\dfrac{1}{12}\\ =-\dfrac{1}{10}\)
\(d,\dfrac{-1^3}{15}+\left(-\dfrac{2}{3}\right)^2:2\dfrac{2}{3}-\left(-\dfrac{5}{6}\right)\\ =-\dfrac{1}{15}+\dfrac{4}{9}\cdot\dfrac{3}{8}+\dfrac{5}{6}\\ =-\dfrac{1}{15}+\dfrac{1}{6}+\dfrac{5}{6}\\ =\dfrac{1}{10}+\dfrac{5}{6}\\ =\dfrac{14}{15}\)
`e,` Không hiểu đề á c: )
Câu 1:
1; 125 : 52
= 53 : 52
= 51
2; 275 : 813
= (33)5 : (34)3
= 315 : 312
= 33
3; 84.165.32
= (23)4.(24)5.25
= 212.220.25
= 237
Câu 1
4; 274.8110
= (33)4.(34)10
= 312.340
= 352