1.Tính giá trị biểu thức:
a/\(42.53+47.156-47\)
b/\(\left[160.\left(730-700\right):2^4-4^2\right].13\)
c/\(4524-\left(864-999\right)-\left(36+3999\right)\)
d/\(2.51^2:17^2+2017^0\)
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HP
15 tháng 4 2021
\(P=\left[tan\dfrac{17\pi}{4}+tan\left(\dfrac{7\pi}{2}-x\right)\right]^2+\left[cot\dfrac{13\pi}{4}+cot\left(7\pi-x\right)\right]^2\)
\(=\left[tan\dfrac{\pi}{4}+tan\left(-\dfrac{\pi}{2}-x\right)\right]^2+\left[cot\left(-\dfrac{3\pi}{4}\right)+cot\left(-\pi-x\right)\right]^2\)
\(=\left[tan\dfrac{\pi}{4}-cotx\right]^2+\left[tan\dfrac{\pi}{4}-cotx\right]^2\)
\(=2\left(1-cotx\right)^2\)
7 tháng 1
a: \(A=\dfrac{9^4}{3^2}=\dfrac{\left(3^2\right)^4}{3^2}=\dfrac{3^8}{3^2}=3^6\)=729
b: \(B=81\left(\dfrac{5}{3}\right)^4=81\cdot\dfrac{5^4}{3^4}=\dfrac{81}{3^4}\cdot5^4=5^4=625\)
c: \(C=\left(\dfrac{4}{7}\right)^{-4}\cdot\left(\dfrac{2}{7}\right)^3\)
\(=\left(\dfrac{7}{4}\right)^4\cdot\left(\dfrac{2}{7}\right)^3\)
\(=\dfrac{7^4}{4^4}\cdot\dfrac{2^3}{7^3}\)
\(=\dfrac{2^3}{4^4}\cdot7\)
\(=\dfrac{2^3}{2^8}\cdot7=\dfrac{7}{2^5}=\dfrac{7}{32}\)
d: \(D=7^{-6}\cdot\left(\dfrac{2}{3}\right)^0\left(\dfrac{7}{5}\right)^6\)
\(=7^{-6}\left(\dfrac{7}{5}\right)^6\)
\(=\dfrac{1}{7^6}\cdot\dfrac{7^6}{5^6}=\dfrac{1}{5^6}=\dfrac{1}{15625}\)
e: \(E=8^3:\left(\dfrac{2}{3}\right)^5\cdot\left(\dfrac{1}{3}\right)^2\)
\(=2^6:\dfrac{2^5}{3^5}\cdot\dfrac{1}{3^2}\)
\(=2^6\cdot\dfrac{3^5}{2^5}\cdot\dfrac{1}{3^2}\)
\(=\dfrac{2^6}{2^5}\cdot\dfrac{3^5}{3^2}=3^3\cdot2=54\)
f: \(F=\left(\dfrac{7}{9}\right)^{-2}\cdot\left(\dfrac{1}{\sqrt{3}}\right)^8\)
\(=\left(\dfrac{9}{7}\right)^2\cdot\left(\dfrac{1}{3}\right)^4\)
\(=\dfrac{9^2}{7^2}\cdot\dfrac{1}{3^4}=\dfrac{9^2}{3^4}\cdot\dfrac{1}{7^2}=\dfrac{81}{81}\cdot\dfrac{1}{49}=\dfrac{1}{49}\)
g: \(G=\left(-\dfrac{4}{5}\right)^{-2}\cdot\left(\dfrac{2}{5}\right)^2\cdot\left(\sqrt{2}\right)^3\)
\(=\left(-\dfrac{5}{4}\right)^2\cdot\left(\dfrac{2}{5}\right)^2\cdot2\sqrt{2}\)
\(=\dfrac{25}{16}\cdot\dfrac{4}{25}\cdot2\sqrt{2}=\dfrac{4}{16}\cdot2\sqrt{2}=\dfrac{8\sqrt{2}}{16}=\dfrac{\sqrt{2}}{2}\)
H9
HT.Phong (9A5)
CTVHS
18 tháng 8 2023
a) \(\left(\dfrac{3}{4}\right)^{-2}\cdot3^2\cdot12^0=16\)
b) \(\left(\dfrac{1}{12}\right)^{-1}\cdot\left(\dfrac{2}{3}\right)^{-2}=27\)
c) \(\left(2^{-2}\cdot5^2\right)^{-2}:\left(5\cdot5^{-5}\right)=16\)
NN
26 tháng 3 2017
\(A=\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right)...\left(1-\frac{1}{2017^2}\right)\)
\(=\frac{1.3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}...\frac{2016.2018}{2017^2}\)
\(=\frac{2.3^2.4^2.5^2...2016^2.2017.2018}{2^2.3^2.4^2.5^2...2017^2}\)
\(=\frac{2018}{2.2017}=\frac{1009}{2017}\)
5 tháng 4 2017
C\(\frac{1}{1}-\frac{1}{2.3}+\frac{1}{3.4}-\frac{1}{4.5}+\frac{1}{5.6}\)-\(\frac{1}{6.7}\)+\(\frac{1}{7.8}\)-\(\frac{1}{8.9}+\frac{1}{9.10}\)
c=\(\frac{1}{1}-\frac{1}{10}\)
c=\(\frac{9}{10}\)
còn a và b rễ lắm mình ko thích làm bài rễ đâu bạn cố chờ lời giải khác nhé!
1 tháng 7 2022
a: \(A=\dfrac{3^6\cdot3^8\cdot5^4-3^{13}\cdot5^{13}\cdot5^{-9}}{3^{12}\cdot5^6+5^6\cdot3^{12}}\)
\(=\dfrac{3^{14}\cdot5^4-3^{13}\cdot5^4}{2\cdot3^{12}\cdot5^6}\)
\(=\dfrac{3^{13}\cdot5^4\cdot\left(3-1\right)}{2\cdot3^{12}\cdot5^6}=\dfrac{3}{5^2}=\dfrac{3}{25}\)
c: \(C=\dfrac{\dfrac{27}{64}+\dfrac{125}{64}-5\cdot\dfrac{16-15}{12}}{\dfrac{25}{64}+\dfrac{4}{9}-\dfrac{5}{6}}\)
\(=\dfrac{47}{24}:\dfrac{1}{576}=47\cdot24=1128\)
7 tháng 1
a: \(A=2^{\dfrac{1}{3}}\cdot2^{\dfrac{2}{3}}=2^{\dfrac{1}{3}+\dfrac{2}{3}}=2^{\dfrac{3}{3}}=2^1=2\)
b: \(B=36^{\dfrac{3}{2}}=\left(6^2\right)^{\dfrac{3}{2}}=6^{2\cdot\dfrac{3}{2}}=6^3=216\)
c: \(C=36^{\dfrac{3}{2}}\cdot\left(\dfrac{1}{6}\right)^2=\left(6^2\right)^{\dfrac{3}{2}}\cdot\dfrac{1}{6^2}=\dfrac{6^{2\cdot\dfrac{3}{2}}}{6^2}=\dfrac{6^3}{6^2}=6\)
d: \(D=\sqrt{81}\cdot\left(\dfrac{1}{3}\right)^2=9\cdot\dfrac{1}{3^2}=9\cdot\dfrac{1}{9}=1\)
e: \(E=\left(3+2\sqrt{2}\right)^{50}\cdot\left(3-2\sqrt{2}\right)^{50}\)
\(=\left[\left(3+2\sqrt{2}\right)\left(3-2\sqrt{2}\right)\right]^{50}\)
\(=\left(9-8\right)^{50}=1^{50}=1\)
f: \(F=120^{\sqrt{5}+1}\cdot120^{3-\sqrt{5}}\)
\(=120^{\sqrt{5}+1+3-\sqrt{5}}=120^4\)
g: \(G=\left(3+2\sqrt{2}\right)^{2019}\cdot\left(3\sqrt{2}-4\right)^{2018}\)
\(=\left(3+2\sqrt{2}\right)^{2018}\cdot\left(3\sqrt{2}-4\right)^{2018}\cdot\left(3+2\sqrt{2}\right)\)
\(=\left[\left(3+2\sqrt{2}\right)\left(3\sqrt{2}-4\right)\right]^{2018}\left(3+2\sqrt{2}\right)\)
\(=\left(9\sqrt{2}-12+12-8\sqrt{2}\right)^{2018}\cdot\left(3+2\sqrt{2}\right)\)
\(=\left(\sqrt{2}\right)^{2018}\cdot\left(3+2\sqrt{2}\right)=2^{\dfrac{1}{2}\cdot2018}\cdot\left(3+2\sqrt{2}\right)\)
\(=2^{1009}\cdot\left(3+2\sqrt{2}\right)\)
@Nguyễn Huy Tú