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BÀI 1.
\(\frac{\left(0,8\right)^5}{\left(0,4\right)^6}=\frac{\left(\frac{4}{5}\right)^5}{\left(\frac{2}{5}\right)^6}=\frac{\frac{4^5}{5^5}}{\frac{2^6}{5^6}}=\frac{4^5}{5^5}:\frac{2^6}{5^6}=\frac{4^5}{5^5}\cdot\frac{5^6}{2^6}=\frac{4^5\cdot5^6}{5^5\cdot2^6}=\frac{4^5\cdot5}{2^6}=\frac{\left(2^2\right)^5\cdot5}{2^6}=\frac{2^{10}\cdot5}{2^6}\) \(=2^4\cdot5=16\cdot5=80\)
BÀI 2.
\(\frac{2^{15}\cdot9^4}{6^6\cdot8^3}=\frac{2^{15}\cdot\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^3}=\frac{2^{15}\cdot3^8}{2^6\cdot3^6\cdot2^9}=\frac{2^{15}\cdot3^8}{2^{15}\cdot3^6}=\frac{3^8}{3^6}=\frac{3^6\cdot3^2}{3^6}=3^2=9\)
mày muốn gì sao mày ra đề khó thế lần sau ra đề dễ hơn đấy
a, Tự chép đề bài ((:
\(=\frac{1}{9}\cdot1+\left(-\frac{1}{243}\right)\cdot\frac{9}{2}\)
\(=\frac{1}{9}-\frac{1}{54}\)
\(=\frac{5}{54}\)
b, 1. \(\left(\frac{2^2\cdot2^3}{4^2\cdot16}\right)^{15}\)
\(=\left(\frac{2^5}{2^4\cdot2^4}\right)^5=\left(\frac{2^5}{2^8}\right)^5=\left(\frac{1}{2^3}\right)^5=\left(\frac{1}{8}\right)^5=\frac{1}{8^5}\)(Để vậy đi :v)
2. \(\left(\frac{2^6}{16^2}\right)^{10}\)
\(=\left(\frac{2^6}{2^8}\right)^{10}=\left(\frac{1}{2^2}\right)^{10}=\frac{1}{2^{20}}\)
c, \(\frac{2^{15}\cdot9^4}{6^6\cdot8^3}\)
\(=\frac{2^{15}\cdot\left(3^2\right)^4}{\left(2\cdot3\right)^6\cdot\left(2^3\right)^3}=\frac{2^{15}\cdot3^8}{2^6\cdot3^6\cdot2^9}=\frac{2^{15}\cdot3^8}{2^{15}\cdot3^6}=\frac{3^2}{1}=3^2=9\)
bài này không khó. Nhưng đánh máy để giải cho bạn thì thực sự khó
a, Ta có: \(\frac{0,8^5}{0,4^6}=\frac{\left(0,4.2\right)^5}{0,4^6}=\frac{0,4^5.2^5}{0,4^6}\) \(=\frac{2^5}{0,4}=80\)
b, Ta có: \(\frac{8^{10}+4^{10}}{8^4+4^{11}}=\frac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}\) \(=\frac{2^{30}+2^{20}}{2^{12}+2^{22}}=\frac{2^{12}\left(2^{18}+2^8\right)}{2^{12}\left(1+2^{10}\right)}\)
\(=\frac{2^{18}+2^8}{1+2^{10}}=\frac{2^8\left(2^{10}+1\right)}{2^{10}+1}=2^8\)
c, Ta có: \(\frac{2^{15}.9^4}{6^3.8^3}=\frac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^3.\left(2^3\right)^3}=\frac{2^{15}.3^8}{2^3.3^3.2^9}\) \(=\frac{2^{15}.3^8}{2^{12}.3^3}=2^3.3^5=1944\)
b)\(\frac{8^{10}+4^{10}}{8^4+4^{11}}\)=\(\frac{\left(2.4\right)^{10}+4^{10}}{\left(2.4\right)^{10}+4^{11}}\)=\(\frac{2^{10}.4^{10}+4^{10}.1}{2^{10}.4^{10}+4^{10}.4}\)=\(\frac{4^{10}\left(2^{10}+1\right)}{4^{10}\left(2^{10}+4\right)}\)=\(\frac{4^{10}.1025}{4^{10}.1028}\)=\(\frac{1025}{1028}\)
a) Vì (2x - 5)2000 và (3y + 4)2002 đều có số mũ là chẵn => (2x - 5)2000 \(\ge\) 0; (3y + 4)2002 \(\ge\) 0
Mà tổng trên lại \(\le\) 0
=> (2x - 5)2000 = (3y + 4)2002 = 0
=> 2x - 5 = 3y + 4 = 0
=> x = 2,5; y = \(\frac{-4}{3}\)
b) x = 18 - 0,8 : \(\frac{1,5}{\frac{3}{2}.\frac{4}{10}.\frac{50}{2}}\)+ \(\frac{1}{4}\)+ \(\frac{1+0,5.4}{6-\frac{46}{23}}\)
= 18 - \(\frac{8}{10}:\frac{1,5}{15}+\frac{1}{4}+\frac{3}{4}\)
= \(18-8+1=11\)
a: \(=\dfrac{-3^4\cdot2^8}{2^2\cdot2^2\cdot3^2}=-3^2\cdot2^2=-6^2=-36\)
b: \(=\dfrac{3^6\cdot2^{15}}{3^6\cdot2^6\cdot2^{15}}=\dfrac{1}{2^6}=\dfrac{1}{64}\)
c: \(=\left(\dfrac{0.8}{0.4}\right)^5\cdot\dfrac{1}{0.4}=2^5\cdot\dfrac{1}{0.4}=\dfrac{32}{0.4}=80\)
Ta có: \(\frac{0,8:\left(\frac{4}{5}\cdot1,25\right)}{0,64-\frac{1}{25}}+\frac{\left(1,08-\frac{2}{25}\right):\frac{4}{7}}{\left(6\frac{5}{9}-3\frac{1}{4}\right)\cdot2\frac{2}{17}}+\frac{\left(1,2\cdot0,5\right)}{\frac{4}{5}}\)
\(=\frac{\frac{4}{5}:\left(\frac{4}{5}\cdot\frac{5}{4}\right)}{\frac{16}{25}-\frac{1}{25}}+\frac{\left(\frac{27}{25}-\frac{2}{25}\right)\cdot\frac{7}{4}}{\left(\frac{59}{9}-\frac{13}{4}\right)\cdot\frac{36}{17}}+\frac{6}{5}\cdot\frac{1}{2}\cdot\frac{5}{4}\)
\(=\frac{\frac{4}{5}}{\frac{3}{5}}+\frac{\frac{7}{4}}{\frac{119}{36}\cdot\frac{36}{17}}+\frac{3}{4}\)
\(=\frac{4}{5}\cdot\frac{5}{3}+\frac{7}{4}\cdot\frac{1}{7}+\frac{3}{4}=\frac{4}{3}+\frac{1}{4}+\frac{3}{4}=\frac{7}{3}\)