BÀI 4 : RÚT GỌN
\(B=\frac{\left(5^4\right)-\left(5^3\right)}{125}\)
Rút gọn:
a) \(\left(\frac{3}{4}\right)^{45}:\left(\frac{9}{6}\right)^{10}\)
b) \(\frac{125^{100}.2^{160}}{5^{298}.4^{80}}\)
a) \(\left(\frac{3}{4}\right)^{45}:\left(\frac{9}{6}\right)^{10}\)
\(=\left(\frac{3}{4}\right)^{45}:\left(\frac{3}{4}\right)^{20}\)
\(=\left(\frac{3}{4}\right)^{25}\)
b) \(\frac{125^{100}.2^{160}}{5^{298}.4^{80}}\)
\(=\frac{5^{300}.2^{160}}{5^{298}.2^{160}}\)
\(=5^2=25\)
a) \(\left(\frac{3}{4}\right)^{45}:\left(\frac{9}{6}\right)^{10}\)
\(\Leftrightarrow\frac{\left(\frac{3}{4}\right)^{45}}{\frac{3^{10}}{2^{10}}}=\frac{\frac{3^{45}}{4^{45}}}{\frac{3^{10}}{2^{10}}}=\frac{3^{45}.2^{10}}{4^{45}}=\frac{3^{35}.2^{10}}{2^{90}}=\frac{3^{35}}{2^{80}}\)
\(\Rightarrow\left(\frac{3}{4}\right)^{45}:\left(\frac{9}{6}\right)^{10}=\frac{3^{35}}{2^{80}}\)
125100.2160/5298.480
=5300.2160/5298.2160
=52=25
k mik nha
Tính và rút gọn các bài toán nâng cao sau
1.Tính
\(A=\left(1-\frac{1}{5}\right).\left(1-\frac{2}{5}\right).\left(1-\frac{3}{5}\right)...\left(1-\frac{9}{5}\right)\)
2 rút gọn
\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{50}\right)\)
Ai nhanh ai đúng mk sẽ tick :) :D
1. Có 1 thừa số là \(1-\frac{5}{5}=0\) nên tích sẽ bằng 0
2.\(B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.......\frac{49}{50}=\frac{1}{50}\)
Bài 1: Rút gọn các biểu thức sau:
a) \(M=3\left|x-2\right|+5\left(4+\frac{4}{5}\right).\)
b) \(N=\left|x-15\right|+4\left|x-19\right|\)
Bài 2: Tìm x,y thuộc Q:
\(\left|x+y-\frac{1}{100}\right|=-\left|x\right|-\left|y\right|-\left|\frac{1}{10}\right|\)
Bài 1: Rút gọn biểu thức
\(A=\frac{2^{10}.13+2^{10}.65}{2^8.104}\) \(B=\frac{15.3^{11}+4.27^4}{9^7}\) \(C=\left(125^3.7^5-175^5:5\right):2016^{2017}\)
Bài 2: Tìm x:
a)\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{x.\left(x+3\right)}=\frac{6}{19}\)b)\(\left|\frac{3}{13}x^2+\frac{1}{2}\right|-\frac{3}{4}=\frac{5}{6}\)
Bài 1: Rút gọn biểu thức
\(A=\frac{2^{10}.13+2^{10}.65}{2^8.104}\) \(B=\frac{15.3^{11}+4.27^4}{9^7}\) \(C=\left(125^3.7^5-175^5:5\right):2016^{2017}\)
Bài 2: Tìm x:
a)\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{x.\left(x+3\right)}=\frac{6}{19}\)b)\(\left|\frac{3}{13}x^2+\frac{1}{2}\right|-\frac{3}{4}=\frac{5}{6}\)
Rút gọn biểu thức:
a) \(\frac{2.8^4.27^2+4.6^9}{2^7.6^7+2^7.40.9^4}\)
b) \(\frac{\left(\frac{2}{3}\right)^3.\left(\frac{-3}{4}\right)^2.\left(-1\right)^5}{\left(\frac{2}{5}\right)^2.\left(\frac{-5}{12}\right)^3}\)
a, \(\dfrac{2\cdot8^4\cdot27^2+4\cdot6^9}{2^7\cdot6^7+2^7\cdot40\cdot9^4}\)
=\(\dfrac{2\cdot\left(2^3\right)^4\cdot\left(3^3\right)^2+2^2\cdot2^9\cdot3^9}{2^7\cdot2^7\cdot3^7+2^7\cdot2^3\cdot5\cdot\left(3^2\right)^4}\)
=\(\dfrac{2\cdot2^{12}\cdot3^6+2^{11}\cdot3^9}{2^{14}\cdot3^7+2^{10}\cdot5\cdot3^8}\)
=\(\dfrac{2^{11}\cdot3^6\cdot\left(2^2+3^3\right)}{2^{10}\cdot3^7\cdot\left(2^4+5\cdot3\right)}\)
=\(\dfrac{2^{11}\cdot3^6\cdot31}{2^{10}\cdot3^7\cdot31}\)
=\(\dfrac{2}{3}\)
b, \(\dfrac{\dfrac{8}{27}\cdot\dfrac{9}{16}\cdot\left(-1\right)}{\dfrac{4}{25}\cdot\dfrac{-125}{1728}}\)
=\(\dfrac{\dfrac{8\cdot9\cdot\left(-1\right)}{27\cdot16}}{\dfrac{4\cdot\left(-125\right)}{25\cdot1728}}\)
=\(\dfrac{\dfrac{-1}{6}}{\dfrac{-5}{432}}\)
=\(\dfrac{-1}{6}\cdot\dfrac{-432}{5}\)
=\(\dfrac{72}{5}\)
Rút gọn biểu thức :
B=\(\left(\frac{3}{5}\right)^2.5^2-\left(2\frac{1}{4}\right)^3:\left(\frac{3}{4}\right)^3+\frac{1}{2}\)
\(B=\left(\frac{3}{5}\right)^2\cdot5^2-\left(2\frac{1}{4}\right)^3:\left(\frac{3}{4}\right)^3+\frac{1}{2}\)
\(B=\left(\frac{3}{5}\cdot5\right)^2-\left(\frac{9}{4}:\frac{3}{4}\right)^3+\frac{1}{2}\)
\(B=3^2-\left(\frac{9}{4}\cdot\frac{4}{3}\right)^3+\frac{1}{2}\)
\(B=3^2-3^3+\frac{1}{2}=-18+\frac{1}{2}=-\frac{35}{2}\)
Bài 1: Tìm x biết: a, |2x+5|-|x+3|=0
Bài 2: Rút gọn:
a,\(\frac{3^6+45^4-15^3.4^5}{27^4.25^3+45^6}\)
b,\(\frac{\left(\frac{2}{5}\right)^7.5^7+\left(\frac{16}{3}\right)^3:\left(\frac{4}{9}\right)^3}{2^7.5^2+512}\)
2a) \(\frac{3^6+45^4-15^3.4^5}{27^4.25^3+45^6}\)
= \(\frac{3^6+\left(3^2.5\right)^4-\left(3.5\right)^3.\left(2^2\right)^5}{\left(3^3\right)^4.\left(5^2\right)^3+\left(3^2.5\right)^6}\)
= \(\frac{3^6+3^8.5^4-3^3.5^3.4^{10}}{3^{12}.5^6-3^{12}.5^6}=\frac{3^3.\left(3^3+3^5.5^4-5^3.4^{10}\right)}{0}\)(xem lại đề)
b) \(\frac{\left(\frac{2}{5}\right)^7.5^7+\left(\frac{16}{3}\right)^3:\left(\frac{4}{9}\right)^3}{2^7.5^2+512}\)
= \(\frac{\left(\frac{2}{5}.5\right)^7+\left(\frac{16}{3}:\frac{4}{9}\right)^3}{2^7.5^2+2^9}\)
= \(\frac{2^7+12^3}{2^7\left(5^2+2^2\right)}\)
= \(\frac{2^7+\left(2^2.3\right)^3}{2^7.29}\)
= \(\frac{2^7+2^6.3^3}{2^7.29}\)
= \(\frac{2^6\left(1+27\right)}{2^7.29}=\frac{28}{2.29}=\frac{14}{29}\)
mk xin lỗi bn nhé...mk vt nhầm đề...mk vt lại nha:
2a,\(\frac{3^6+45^4-15^3.9^5}{27^4.25^3+45^6}\)
Rút gọn: \(\frac{\left(\frac{-1}{2}\right)^3-\left(\frac{3}{4}\right)^3.\left(-2\right)^2}{2.\left(-1\right)^5+\left(\frac{3}{4}\right)^2-\frac{3}{8}}\)