a)3/4+1/1/4*2/2/3-(-1/2)^2:6/5

=3/4+5/4*8/3-1/4:6/5

=3/4+10/3-5/24=18/24+80/24-5/24=93/24=31/8

b)(x-1)^5=32=2^5

=>x-1=2

x=2+1

x=3

\(\frac{1}{4}+\frac{3}{8}+\frac{5}{16}=\frac{5}{8}+\frac{5}{16}=\frac{15}{16}\)

\(\frac{3}{5}-\frac{1}{3}-\frac{1}{6}=\frac{4}{15}-\frac{1}{6}=\frac{1}{10}\)

\(\frac{4}{7}\cdot\frac{5}{8}\cdot\frac{7}{12}=\frac{4.5.7}{7.8.12}=\frac{140}{672}=\frac{5}{24}\)

\(\frac{25}{28}:\frac{15}{14}\cdot\frac{6}{7}=\frac{5}{6}\cdot\frac{6}{7}=\frac{5}{7}\)

\(\frac{1}{4}+\frac{3}{8}+\frac{5}{16}=\frac{15}{16}\)

\(\frac{3}{5}-\frac{1}{3}-\frac{1}{6}=\frac{1}{10}\)

\(\frac{4}{7}\times\frac{5}{8}\times\frac{7}{12}=\frac{5}{24}\)

\(\frac{25}{28}:\frac{15}{14}\times\frac{6}{7}=\frac{5}{7}\)

\(\frac{4}{\frac{2}{5}}:\left(-\frac{33}{10}\right)+x=-\frac{1}{\frac{5}{6}}\)

\(10:\left(-\frac{33}{10}\right)+x=-\frac{6}{5}\)

\(-\frac{100}{33}+x=-\frac{6}{5}\)

\(x=\frac{302}{165}\)

Bài 1:

a: \(\frac{5\times7}{15}=\frac{35}{15}=\frac73\)

b: \(8:\frac{16}{23}=8\times\frac{23}{16}=\frac{8}{16}\times23=23\times\frac12=\frac{23}{2}\)

c: \(\frac{8}{15}:5=\frac{8}{15\times5}=\frac{8}{75}\)

d: \(\frac{15}{19}\times3=\frac{15\times3}{19}=\frac{45}{19}\)

Bài 2:

a: \(3\times\frac49+\frac23-\frac{7}{18}\)

\(=\frac43+\frac23-\frac{7}{18}\)

\(=\frac63-\frac{7}{18}=2-\frac{7}{18}=\frac{36}{18}-\frac{7}{18}=\frac{29}{18}\)

b: \(\frac{7}{10}\times\frac23-\frac14=\frac{14}{30}-\frac14=\frac{28}{60}-\frac{15}{60}=\frac{28-15}{60}=\frac{13}{60}\)

c: \(\frac98-\frac78:\frac56=\frac98-\frac78\times\frac65\)

\(=\frac98-\frac{42}{40}=\frac{45}{40}-\frac{42}{40}=\frac{3}{40}\)

d: \(\frac23+\frac12:\frac32-\frac{11}{24}\)

\(=\frac23+\frac12\times\frac23-\frac{11}{24}\)

\(=\frac23+\frac13-\frac{11}{24}=1-\frac{11}{24}=\frac{13}{24}\)

Bài 3:

Độ dài đáy tương ứng với chiều cao là: \(\frac35\times2=\frac65\left(m\right)\)

Chu vi hình bình hành là:

\(\left(\frac65+\frac45\right)\times2=\frac{10}{5}\times2=2\times2=4\left(m\right)\)

Diện tích bình hành là;

\(\frac65\times\frac35=\frac{18}{25}\left(m^2\right)\)

7.6^10.2^20.3^6-2^19.6^15/9.6^19.2^9-4.3^17.2^26

\(a,x^4-4x^3-19x^2+106x-120=0\\ \Rightarrow\left(x-4\right)\left(x^3-19x+30\right)=0\Rightarrow\left(x-4\right)\left(x+5\right)\left(x^2-5x+6\right)=0\\ \Rightarrow\left(x-4\right)\left(x+5\right)\left(x-2\right)\left(x-3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=4\\x=-5\\x=2\\x=3\end{matrix}\right.\)

Vậy pt có tập nghiệm \(S=\left\{-5;2;3;4\right\}\)

\(b,4x^4+12x^3+5x^2-6x-15=0\\ \Rightarrow\left(x-1\right)\left(4x^3+16x^2+21x+15\right)=0\\ \Rightarrow\left(x-1\right)\left[\left(4x^3+10x^2\right)+\left(6x^2+15x\right)+\left(6x+15\right)\right]=0\\ \Rightarrow\left(x-1\right)\left[2x^2\left(2x+5\right)+3x\left(2x+5\right)+3\left(2x+5\right)\right]=0\\ \Rightarrow\left(x-1\right)\left(2x+5\right)\left(2x^2+3x+3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{5}{2}\\2x^2+3x+3=0\left(vô.lí\right)\end{matrix}\right.\)

Vậy pt có tập nghiệm \(S=\left\{1;-\dfrac{5}{2}\right\}\)