a, \(\frac{8^{15^{ }}.3^{16}}{4^{23^{ }}.9^8}=\frac{2^{45}.3^{16}}{2^{46}.3^{16}}=\frac{2^{45}}{2^{46}}=\frac{1}{2}\)
b, \(\sqrt{121}-4.\sqrt{9}+\sqrt{36}=11-4.3+6=11-12+6=5\)
c,
\(\frac{2^5}{5^2}+5\frac{1}{2}.\left(4,5-2,5\right)+\frac{2^3}{-4}+\left(-2016\right)^0\)
\(\frac{4}{25}+\frac{11}{2}.2+\frac{8}{-4}+1=\frac{4}{25}+11+\left(-2\right)+1=\frac{4}{25}+10\)
= \(\frac{254}{25}\)
2 Thực hiện phép tính
\(\frac{17}{9}-\frac{17}{9}:\left(\frac{7}{3}+\frac{1}{2}\right)\)
\(\frac{4}{3}.\frac{2}{5}-\frac{3}{4}.\frac{2}{5}\)
\(-\frac{3}{4}.5\frac{3}{13}-0.75.\frac{36}{13}\)
\(3.\left(-\frac{4}{3}\right)^2-\frac{7}{3}\)
\(-\frac{5}{7}.\frac{3}{11}+\frac{-5}{7}.\frac{8}{11}+3\frac{5}{7}\)
\(32\frac{1}{7}:\left(\frac{-5}{4}\right)-47\frac{1}{7}:\left(\frac{-5}{4}\right)\)
\(\left(\frac{2}{3}+\frac{1}{2}\right)^2-\frac{1}{12}\\ \frac{1}{4}-\frac{5}{12}:\frac{1}{6}+\frac{-6}{5}\\ \frac{17}{21}+\frac{5}{23}-\frac{1}{2}+\frac{4}{21}-1\frac{5}{23}\)
\(\left(-3\right)^2+\sqrt{\frac{16}{25}}-\sqrt{9}+\frac{\sqrt{81}}{3}\)
thực hiện phép tính : ( tính nhanh nếu có thể )
a) \(\left(\frac{11}{12}:\frac{33}{16}\right).\frac{3}{5}+\frac{7}{23}.\left[\left(\frac{-8}{6}+\frac{-45}{18}\right)\right]\)
b) \(\left(\frac{-2}{3}+\frac{3}{7}\right):\frac{4}{5}+\left(\frac{-1}{3}+\frac{4}{7}\right):\frac{4}{5}\)
c) \(\frac{5}{9}:\left(\frac{1}{11}-\frac{5}{22}\right)+\frac{5}{9}:\left(\frac{1}{15}-\frac{2}{3}\right)\)
d) \(\frac{-3}{4}.\frac{12}{-5}.\frac{-25}{6}+\left(-2\right).\frac{-38}{21}.\frac{-7}{4}.\frac{-3}{8}\)
rút gon
a,\(\frac{2.5^{22}-9.5^{21}}{25^{10}}\)
b,\(\frac{5\left(3.7^{15}-19.7^{14}\right)}{7^{16}+3.7^{15}}\)
c,\(\frac{\left(\left(-2\right)^2\right)^3.\left(-4\right)^2}{\left(-2\right)^3.\left(-2\right)^2}\)
d,\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
e,\(2^3+3.\left(\frac{1}{8}\right)^0-\left(\frac{1}{2^2}\right).4+\left[\left(-2\right)^2:\frac{1}{2}\right].8\)
f,\(\frac{\left(\frac{2}{5}\right)^7.5^5+\left(\frac{9}{4}\right)^3:\left(\frac{3}{16}\right)^3}{2^7.5^2+512}\)
Tính giá trị biểu thức:
D = (-2)\(^3\)\(.\left(\frac{3}{4}-0,25\right):\left(2\frac{1}{4}-1\frac{1}{6}\right)\) E = 5\(\sqrt{16}-4\sqrt{9}+\sqrt{25}-0,3\sqrt{400}\)
F = \(\left(-\frac{3}{2}\right)^2+\left|-\frac{5}{6}\right|-1\frac{1}{2}:6\)
Tìm x, y, z
a) \(\sqrt{16}x+\frac{3}{4}=2\sqrt{\frac{4}{25}}+0,01.\sqrt{100}\)
b) \(\left|x\right|+3^2=2^2+\left(\frac{1}{2}\right)^3\)
c) \(2x\left(x-\frac{2}{3}\right)=0\)
d) \(\frac{37-x}{x+13}=\frac{3}{7}\)
Tìm x thỏa mãn:
a) \(2\left|\frac{2}{3}-x\right|+\frac{1}{4}=\frac{3}{4}\)
b) \(8\sqrt{x}+2x-9=5x+7+6\sqrt{x}-3x-12\)
c) \(2x^2+5x+8+\sqrt{x}=x^2+3x+35+x^2+2x-7\)
1) Tính:
a) \(\frac{\left(1+\frac{17}{1}\right).\left(1+\frac{17}{2}\right).\left(1+\frac{17}{3}\right).....\left(1+\frac{17}{19}\right)}{\left(1+\frac{19}{1}\right).\left(1+\frac{19}{2}\right).\left(1+\frac{19}{3}\right).....\left(1+\frac{19}{17}\right)}\)
b) \(\frac{\frac{-6}{5}+\frac{6}{19}-\frac{6}{23}}{\frac{9}{5}-\frac{9}{19}+\frac{9}{23}}\)
c) \(\frac{\frac{1}{6}-\frac{1}{39}+\frac{1}{51}}{\frac{1}{8}-\frac{1}{52}+\frac{1}{68}}\)
d) \(\frac{\frac{2}{3}-\frac{2}{5}-\frac{2}{7}+\frac{2}{11}}{\frac{13}{3}-\frac{13}{5}-\frac{13}{7}+\frac{13}{11}}\)
e) \(\frac{\frac{1}{1009}+\frac{1}{1010}+\frac{1}{1011}+...+\frac{1}{2017}}{1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2015}-\frac{1}{2016}+\frac{1}{2017}}\)
2) CMR: \(\frac{1}{2^2}+\frac{1}{2^4}+\frac{1}{2^6}+...+\frac{1}{2^{800}}< \frac{1}{3}\)
\(A=4\frac{1}{3}+\left(\frac{-1}{3}\right)^2-\frac{\sqrt{100}}{15}-\frac{7}{9}\)
Thực hiện phép tính:
a) \(\frac{11}{24}-\frac{5}{41}+\frac{13}{24}+0,5-\frac{36}{41}\)
b)\(-12:\left(\frac{3}{4}-\frac{5}{6}\right)^2\)
c)\(\frac{7}{23}.\left[\left(\frac{-8}{6}\right)-\frac{45}{18}\right]\)
d)\(23\frac{1}{4}.\frac{7}{5}-13\frac{1}{4}:\frac{5}{7}\)
e)\(\left(1+\frac{2}{3}-\frac{1}{4}\right).\left(0,8-\frac{3}{4}\right)^2\)
