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Có: 7-3.\(\frac{-1}{4}^2\)
= 7-3. \(\frac{1}{16}\)
= 7- \(\frac{3}{16}\)
= \(\frac{112}{16}\)-\(\frac{3}{16}\)
= \(\frac{109}{16}\)
\(\frac{1}{2}.2^n+2^{2+n}=9.2^5\)
\(\frac{1}{2}.2^n+4.2^n=9.2^5\)
\(2^n.\left(\frac{1}{2}+4\right)=9.2^5\)
\(2^n.\frac{9}{2}=9.2^5\)
\(2^n=9.\frac{2}{9}.2^5\)
\(2^n=2.2^5\)
\(2^n=2^6\)
\(\Rightarrow n=6\)
\(\frac{1}{2}\)\(\times\)\(2^n\)\(+\)\(2^{2+n}\)\(=\)\(9\)\(\times\)\(2^5\)
\(\frac{1}{2}\)\(\times\)\(2^n\)\(\times\)\((\)\(1\)\(+\)\(2^2\)\()\)\(=\)\(9\)\(\times\)\(2^5\)
\(\frac{1}{2}\)\(\times\)\(2^n\)\(\times\)\(5\)\(=\)\(9\)\(\times\)\(2^5\)
\(2^n\)\(=\)\(9\)\(\times\)\(32\)\(\div\)\(5\)\(\times\)\(2\)
\(2^n\)\(=\)115,2
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
a) \(\frac{75^3.3^7}{81^4.5^6}=\frac{5^3.3^3.5^3.3^7}{\left(3^4\right)^4.5^6}=\frac{5^6.3^3.3^7}{3^{16}.5^6}=\frac{3^{10}}{3^{16}}=\frac{1}{3^6}=\frac{1}{729}\)
b) \(\frac{6^6.4^2}{3^{12}.2^8}=\frac{2^6.3^6.\left(2^2\right)^2}{3^{12}.2^8}=\frac{2^6.3^6.2^4}{3^{12}.2^8}=\frac{2^{10}.3^6}{3^{12}.2^8}=\frac{2^2.1}{3^6}=\frac{4}{729}\)
c) \(\frac{34^5.2^5}{2^{14}.17^5}=\frac{2^5.17^5.2^5}{2^{14}.17^5}=\frac{2^{10}}{2^{14}}=\frac{1}{2^4}=\frac{1}{16}\)
\(=\left(\dfrac{1}{2}\right)^{n+7+\dfrac{1}{3}n+\dfrac{1}{2}}=\left(\dfrac{1}{2}\right)^{\dfrac{4}{3}n+\dfrac{15}{2}}\)