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Bài 1
\(a,\left(\frac{3}{5}\right)^2-\left[\frac{1}{3}:3-\sqrt{16}.\left(\frac{1}{2}\right)^2\right]-\left(10.12-2014\right)^0\)
\(=\frac{9}{25}-\left[\frac{1}{9}-4.\frac{1}{4}\right]-1\)
\(=\frac{9}{25}-\left(-\frac{8}{9}\right)-1\)
\(=\frac{9}{25}+\frac{8}{9}-1\)
\(=\frac{56}{225}\)
\(b,|-\frac{100}{123}|:\left(\frac{3}{4}+\frac{7}{12}\right)+\frac{23}{123}:\left(\frac{9}{5}-\frac{7}{15}\right)\)
\(=\frac{100}{123}:\left(\frac{4}{3}\right)+\frac{23}{123}:\frac{4}{3}\)
\(=\left(\frac{100}{123}+\frac{23}{123}\right):\frac{4}{3}\)
\(=1:\frac{4}{3}=\frac{3}{4}\)
Phần c đăng riêng vì mk chưa tìm đc cách giải bt mỗi đáp án :v
\(c,\frac{\left(-5\right)^{32}.20^{43}}{\left(-8\right)^{29}.125^{25}}\)
\(=\frac{\left(-5\right)^{32}.\left(4.5\right)^{43}}{\left[4.\left(-2\right)\right]^{29}.\left(-5^3\right)^{25}}\)
\(=\frac{-5^{32}.4^{43}.5^{43}}{4^{29}.\left(-2\right)^{29}.\left(5\right)^{75}}\)
\(=\frac{\left(-5^4\right)^8.4^{43}.5^{43}}{4^{29}.\left(-2\right)^{29}.\left(5^3\right)^{25}}\)
\(=-\frac{1}{2}\)
\(a,\frac{-5}{9}.\left(\frac{3}{10}-\frac{2}{5}\right)\)
\(=\frac{-5}{9}.\frac{-1}{10}\)
\(=\frac{1}{18}\)
\(b,2^8:2^5+3^3.2-12\)
\(=2^3+9.2-12\)
\(=8+18-12\)
\(=26-12\)
\(=14\)
Câu c,d em chưa học nên không biết làm ạ, mong mọi người thông cảm!!!
Sửa lại câu b
\(=2^3+27.2-12\)
\(=8+54-12\)
\(=62-12\)
\(=50\)
\(=\left(8+2.4\right)\left(5.25:7\right):\left\{\left[\dfrac{15}{7}+\dfrac{5}{7}\right]:\left[4:\dfrac{8}{9}\right]\right\}\)
\(=10.4\cdot\dfrac{3}{4}:\left\{\dfrac{20}{7}:\dfrac{9}{2}\right\}\)
\(=7.8:\dfrac{40}{63}=12.285\)
a) \(\frac{3}{5}:\left(\frac{-1}{15}-\frac{1}{6}\right)+\frac{3}{5}:\left(\frac{-1}{3}-1\frac{1}{15}\right)\)
\(=\frac{3}{5}:\frac{-7}{30}+\frac{3}{5}:\frac{-7}{5}\)
\(=\frac{3}{5}\cdot\frac{30}{-7}+\frac{3}{5}\cdot\frac{5}{-7}\)
\(=\frac{3}{5}\left(\frac{-30}{7}+\frac{-5}{7}\right)=\frac{3}{5}\cdot-5=-3\)
b) \(10\cdot\sqrt{0,01}\cdot\sqrt{\frac{16}{9}}+3\sqrt{49}-\frac{1}{6}\sqrt{4}\)
\(=10\cdot\frac{1}{10}\cdot\frac{4}{3}+3\cdot7-\frac{1}{6}\cdot2\)
\(=\frac{4}{3}+21-\frac{2}{6}=22\)
a) \(\sqrt{0,01}+\sqrt{0,16}-12^0=0,1+0,4-1=-0,5\)
b) \(\left(\frac{1}{16}\right)^7:\left(\frac{1}{8}\right)^9=\left[\left(\frac{1}{2}\right)^4\right]^7:\left[\left(\frac{1}{2}\right)^3\right]^9=\left(\frac{1}{2}\right)^{28}:\left(\frac{1}{2}\right)^{27}=\frac{1}{2}\)
a)
\(=\sqrt{0,1^2}+\sqrt{0,4^2}-1\)
\(=|0,1|+|0,4|-1\)
\(=0,1+0,4-1=-0,5\)
b)
= \(\left(\left(\frac{1}{2}\right)^4\right)^7:\left(\left(\frac{1}{2}\right)^3\right)^9\)
=\(\left(\frac{1}{2}\right)^{4\cdot7}:\left(\frac{1}{2}\right)^{3\cdot9}\)
= \(\left(\frac{1}{2}\right)^{28}:\left(\frac{1}{2}\right)^{27}\)
\(=\left(\frac{1}{2}\right)^{28-27}\)
\(=\left(\frac{1}{2}\right)^1=\frac{1}{2}\)