câu 3 : 1026

câu 4: 8852

a)

\(\left(\dfrac{2}{5}+\dfrac{3}{4}\right)^2=\left(\dfrac{23}{20}\right)^2=\pm\dfrac{23}{20}\)

b)

\(\left(\dfrac{5}{4}-\dfrac{1}{6}\right)^2=\left(\dfrac{13}{12}\right)^2=\pm\dfrac{13}{12}\)

\(\left(\dfrac{-10}{3}\right)^5.\left(\dfrac{6}{5}\right)^4\\ =\left(\dfrac{-10}{3}\right).\left(\dfrac{10}{3}\right)^4.\left(\dfrac{6}{5}\right)^4\\ =\left(\dfrac{-10}{3}\right).\left(\dfrac{10}{3}.\dfrac{6}{5}\right)^4\\ =\left(\dfrac{-10}{3}\right).4^4\\ =\left(\dfrac{-10}{3}\right).256\\ =\dfrac{-2560}{3}\)

\(\dfrac{8^n}{2^n}=4\\ \Leftrightarrow\left(\dfrac{8}{2}\right)^n=4\\ \Leftrightarrow4^n=4^1\\ \Rightarrow n=1\)

a)

\(x:\left(\dfrac{3}{4}\right)^3=\left(\dfrac{3}{4}\right)^2\\ \Leftrightarrow x=\left(\dfrac{3}{4}\right)^2.\left(\dfrac{3}{4}\right)^3\\ \Leftrightarrow x=\left(\dfrac{3}{4}\right)^5\\ \Rightarrow x=\dfrac{243}{1024}\)

b)

\(\dfrac{2^5}{5}.x=\dfrac{2^8}{5}\\ \Leftrightarrow x=\dfrac{2^8}{5}.\dfrac{5}{2^5}\\ \Leftrightarrow x=2^3\\ \Rightarrow x=8\)

a)

\(\left(\dfrac{1}{5}\right)^5.5^5\\ =\left(\dfrac{1}{5}.5\right)^5\\ =1^5=1\)

b)

\(\left(0,125\right)^3.512\\ =\left(0,125\right)^3.8^3\\ =\left(0,125.8\right)^3\\ =1^3=1\)

c)

\(\left(0,25\right)^4.1024\\ =\left(0,25\right)^4.256.4\\ =\left(0,25\right)^4.4^4\\ =\left(0,25.4\right)^4\\ =1^4.4\\ =4\)

\(\left(2x-1\right)^3=8\\ \Leftrightarrow\left(2x-1\right)^3=2^3\\ \Rightarrow2x-1=2\\ \Leftrightarrow2x=2+1\\ \Leftrightarrow2x=3\\ \Leftrightarrow x=\dfrac{3}{2}\)

\(M=\dfrac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\\ M=\dfrac{\left(2^2\right)^5.\left(3^2\right)^4-2.\left(2.3\right)^9}{2^{10}.3^8+\left(2.3\right)^8.2^2.5}\\ M=\dfrac{2^{10}.3^8-2.2^9.3^9}{2^{10}.3^8+2^8.3^8.2^2.5}\\ M=\dfrac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}\\ M=\dfrac{2^{10}.3^8\left(1-3\right)}{2^{10}.3^8\left(1+5\right)}\\ M=\dfrac{-2}{6}=\dfrac{-1}{3}\)

Chúc bạn học tốt :3

1. So sánh:

a. \(\dfrac{-1}{5}\) và \(\dfrac{1}{1000}\)

Ta có:

\(\dfrac{-1}{5}< 0\\ \dfrac{1}{1000}>0\\ \Rightarrow\dfrac{-1}{5}< \dfrac{1}{1000}\)

b.\(\dfrac{267}{-268}\) và \(\dfrac{-1347}{1343}\)

Ta có:

\(\dfrac{267}{-268}>-1\\ \dfrac{-1347}{1343}< -1\\ \Rightarrow\dfrac{267}{-286}>\dfrac{-1347}{1343}\)

c.\(\dfrac{-13}{38}\) và \(\dfrac{29}{-88}\)

Ta có:

\(\dfrac{-13}{38}< \dfrac{-13}{39}=\dfrac{-1}{3}\\ \dfrac{-29}{88}>\dfrac{-29}{87}=\dfrac{-1}{3}\\ \Rightarrow\dfrac{-13}{38}< \dfrac{-29}{88}\)

Bài 2:

Ta có:

\(\dfrac{1+y}{3}=\dfrac{4+2y}{4}\\ \left(1+y\right).4=\left(4+2y\right).3\\4+4.y=12+6.y\\4y-6y=12-4\\ y\left(4-6\right)=8\\ y.\left(-2\right)=8\\ y=\dfrac{8}{-2}\\ y=-4 \)

Thay y= -4 vào \(\dfrac{4+2y}{4}=\dfrac{1+6y}{x}\)

\(\Rightarrow\dfrac{4+2.\left(-4\right)}{4}=\dfrac{1+6.\left(-4\right)}{x}\\ \dfrac{-4}{4}=\dfrac{-23}{x}\\ -1=\dfrac{-23}{x}\\ -x=-23\\ \Rightarrow x=23\)

Vậy \(x=23\\ y=-4\)