\(\left(\dfrac{1}{16}\right)^{10}=\left[\left(\dfrac{1}{2}\right)^4\right]^{10}=\left(\dfrac{1}{2}\right)^{40}< \left(\dfrac{1}{2}\right)^{50}\\ \left(\dfrac{1}{2}\right)^{300}=\left(\dfrac{1}{2}\right)^{3\cdot100}=\left[\left(\dfrac{1}{2}\right)^3\right]^{100}=\left(\dfrac{1}{8}\right)^{100}\\ \left(\dfrac{1}{3}\right)^{200}=\left(\dfrac{1}{3}\right)^{2\cdot100}=\left[\left(\dfrac{1}{3}\right)^2\right]^{100}=\left(\dfrac{1}{9}\right)^{100}\\ \dfrac{1}{8}>\dfrac{1}{9}\Rightarrow\left(\dfrac{1}{8}\right)^{100}>\left(\dfrac{1}{9}\right)^{100}\Rightarrow\left(\dfrac{1}{2}\right)^{300}>\left(\dfrac{1}{3}\right)^{200}\\ \left(0,3\right)^{20}=\left(0,3\right)^{2\cdot10}=\left[\left(0,3\right)^2\right]^{10}=\left(0,09\right)^{10}< \left(0,1\right)^{10}\)

a) \(\left[\left(\dfrac{1}{2}\right)^4\right]^{10}=\left(\dfrac{1}{2}\right)^{40}\)

\(\Rightarrow\left(\dfrac{1}{2}\right)^{40}< \left(\dfrac{1}{2}\right)^{50}\)

Vì \(40< 50\)

b)\(\left[\left(\dfrac{1}{2}\right)^3\right]^{100}=\left(\dfrac{1}{8}\right)^{100}\)

\(\left[\left(\dfrac{1}{3}\right)^2\right]^{100}=\left(\dfrac{1}{9}\right)^{100}\)

\(\Rightarrow\text{​​}\text{​​}\left(\dfrac{1}{2}\right)^{300}>\left(\dfrac{1}{3}\right)^{200}\)

Vì \(\dfrac{1}{8}>\dfrac{1}{9}\)

c)\(\left[\left(0,3\right)^2\right]^{10}=\left(0,09\right)^{10}\)

\(\Rightarrow\left(0,1\right)^{10}>\left(0,3\right)^{20}\)

Vì \(0,1>0,09\)

Sửa lại câu a

\(\left(\dfrac{1}{2}\right)^{40}>\left(\dfrac{1}{2}\right)^{50}\)

Giải:

a) \(\left(\dfrac{1}{3}.x\right):\dfrac{2}{3}=1\dfrac{3}{4}:\dfrac{2}{5}\)

\(\Leftrightarrow\left(\dfrac{1}{3}x\right):\dfrac{2}{3}=\dfrac{7}{4}:\dfrac{2}{5}\)

\(\Leftrightarrow\left(\dfrac{1}{3}x\right):\dfrac{2}{3}=\dfrac{35}{8}\)

\(\Leftrightarrow\dfrac{1}{3}x=\dfrac{35}{8}.\dfrac{2}{3}\)

\(\Leftrightarrow\dfrac{1}{3}x=\dfrac{35}{12}\)

\(\Leftrightarrow x=\dfrac{35}{12}:\dfrac{1}{3}\)

\(\Leftrightarrow x=\dfrac{35}{4}\)

Vậy \(x=\dfrac{35}{4}\).

b) \(4,5:0,3=2,25\left(0,1.x\right)\)

\(\Leftrightarrow15=2,25\left(0,1.x\right)\)

\(\Leftrightarrow2,25\left(0,1.x\right)=15\)

\(\Leftrightarrow0,1.x=\dfrac{15}{2,25}\)

\(\Leftrightarrow0,1.x=\dfrac{20}{3}\)

\(\Leftrightarrow x=\dfrac{20}{3}:0,1\)

\(\Leftrightarrow x=\dfrac{200}{3}\)

Vậy \(x=\dfrac{200}{3}\).

c) \(8:\left(\dfrac{1}{4}.x\right)=2:0,02\)

\(\Leftrightarrow8:\left(\dfrac{1}{4}.x\right)=100\)

\(\Leftrightarrow\dfrac{1}{4}.x=\dfrac{2}{25}\)

\(\Leftrightarrow x=\dfrac{2}{25}:\dfrac{1}{4}\)

\(\Leftrightarrow x=\dfrac{8}{25}\)

Vậy \(x=\dfrac{8}{25}\).

d) \(3:2\dfrac{1}{4}=\dfrac{3}{4}:\left(6.x\right)\)

\(\Leftrightarrow3:\dfrac{9}{4}=\dfrac{3}{4}:\left(6.x\right)\)

\(\Leftrightarrow\dfrac{4}{3}=\dfrac{3}{4}:\left(6.x\right)\)

\(\Leftrightarrow\dfrac{4}{3}:\left(6.x\right)=\dfrac{3}{4}\)

\(\Leftrightarrow6.x=\dfrac{4}{3}:\dfrac{3}{4}\)

\(\Leftrightarrow6.x=\dfrac{16}{9}\)

\(\Leftrightarrow x=\dfrac{16}{9}:6\)

\(\Leftrightarrow x=\dfrac{8}{27}\)

Vậy \(x=\dfrac{8}{27}\).

Chúc bạn học tốt!!!

a)

b) 4,5 : 0,3 = 2,25 : ( 0,1.x) => 0,1.x =

c)

d)

Bạn hãy chỉ giúp mình cách viết phân số và hỗn số trên máy tính. Mình cảm ơn bạn nhiều lắm!^ - ^

a) Ta có: 10²⁰= (10²)¹⁰=100¹⁰>90¹⁰

^{\(\Rightarrow\)}10²⁰>90¹⁰

b) Ta có: (-5)³⁰ = (-5³)¹⁰ =(-125)¹⁰
và (-3)⁵⁰ = (-3⁵)¹⁰ = (-243)¹⁰
Mà (-125)¹⁰ < (-243)¹⁰ => (-5)¹⁰ < (-3)⁵⁰

c)- 0,3²⁰=(0,3²)¹⁰=0,09¹⁰.

Do 0,09<0,1 =>0,09¹⁰<0,1¹⁰.

=>0,1¹⁰>0,3²⁰.

d) Ta có : \(\left(\dfrac{1}{16}\right)^{10}=\left(\dfrac{1}{2^4}\right)^{10}=\dfrac{1}{2^{40}}\)

\(\left(\dfrac{1}{2}\right)^{50}=\dfrac{1}{2^{50}}\)

Vì \(2^{40}< 2^{50}\Rightarrow\dfrac{1}{2^{40}}>\dfrac{1}{2^{50}}\Rightarrow\left(\dfrac{1}{16}\right)^{10}>\left(\dfrac{1}{2}\right)^{50}\)

\(\dfrac{8^{14}}{4^4.64^5}=\dfrac{\left(2^3\right)^{14}}{\left(2^2\right)^4.\left(2^5\right)^5}=\dfrac{2^{42}}{2^8.2^{25}}=2^{42-\left(8+25\right)}=2^9\)

\(\dfrac{9^{10}.27^7}{81^7.3^{15}}=\dfrac{\left(3^2\right)^{10}.\left(3^3\right)^7}{\left(3^4\right)^7.3^{15}}=\dfrac{3^{20}.3^{21}}{3^{28}.3^{15}}=\dfrac{3^{20+21}}{3^{28+15}}=\dfrac{3^{41}}{3^{41}.3^2}=\dfrac{1}{3^2}=\dfrac{1}{9}\)

Ta có :

\(0,0\left(8\right)=\dfrac{1}{10}.0,\left(8\right)=\dfrac{1}{10}.0,\left(1\right).8=\dfrac{1}{10}.\dfrac{1}{9}.8=\dfrac{4}{45}\)

\(0,1\left(2\right)=0,1+0,0\left(2\right)\)

\(=\dfrac{1}{10}+\dfrac{1}{10}.0,\left(2\right)=\dfrac{1}{10}+\dfrac{1}{10}.0,\left(1\right).2\)

\(=\dfrac{1}{10}+\dfrac{1}{10}.\dfrac{1}{9}.2=\dfrac{9}{90}+\dfrac{2}{90}=\dfrac{11}{90}\)

\(0,1\left(23\right)=0,1+0,0\left(23\right)=\dfrac{1}{10}+\dfrac{1}{10}.0,23\)

\(=\dfrac{1}{10}+\dfrac{1}{10}.0,\left(01\right).23\)

\(\dfrac{1}{10}+\dfrac{1}{10}.\dfrac{1}{99}.23=\dfrac{99}{990}+\dfrac{23}{990}=\dfrac{122}{990}=\dfrac{61}{495}\)

\(\dfrac{34}{99};\dfrac{5}{9};\dfrac{41}{333}.\)

Xin lỗi, câu trả lời của em nhầm với bài 88. Đáp án sửa lại là :

\(\dfrac{4}{45};\dfrac{11}{90};\dfrac{61}{495}.\)

a: \(A=3^{\dfrac{2}{5}}\cdot3^{\dfrac{1}{5}}\cdot3^{\dfrac{1}{5}}=3^{\dfrac{2}{5}+\dfrac{1}{5}+\dfrac{1}{5}}=3^{\dfrac{4}{5}}\)

b: \(B=\left(-27\right)^{\dfrac{1}{3}}=\left[\left(-3\right)^3\right]^{\dfrac{1}{3}}=\left(-3\right)^{\dfrac{1}{3}\cdot3}=\left(-3\right)^1=-3\)

c: \(C=\sqrt[3]{-64}\cdot\left(\dfrac{1}{2}\right)^3\)

\(=\sqrt[3]{\left(-4\right)^3}\cdot\dfrac{1}{2^3}=-4\cdot\dfrac{1}{8}=-\dfrac{4}{8}=-\dfrac{1}{2}\)

d: \(D=\left(-27\right)^{\dfrac{1}{3}}\cdot\left(\dfrac{1}{3}\right)^4\)

\(=\left[\left(-3\right)^3\right]^{\dfrac{1}{3}}\cdot\dfrac{1}{3^4}\)

\(=\left(-3\right)^{3\cdot\dfrac{1}{3}}\cdot\dfrac{1}{81}=\dfrac{-3}{81}=\dfrac{-1}{27}\)

e: \(E=\left(\sqrt{3}+1\right)^{106}\cdot\left(\sqrt{3}-1\right)^{106}\)

\(=\left[\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)\right]^{106}\)

\(=\left(3-1\right)^{106}=2^{106}\)

f: \(F=360^{\sqrt{5}+1}\cdot20^{3-\sqrt{5}}\cdot18^{3-\sqrt{5}}\)

\(=360^{\sqrt{5}+1}\cdot\left(20\cdot18\right)^{3-\sqrt{5}}\)

\(=360^{\sqrt{5}+1}\cdot360^{3-\sqrt{5}}=360^{\sqrt{5}+1+3-\sqrt{5}}=360^4\)

g: \(G=2023^{3+2\sqrt{2}}\cdot2023^{2\sqrt{2}-3}\)

\(=2023^{3+2\sqrt{2}+2\sqrt{2}-3}\)

\(=2023^{4\sqrt{2}}\)

a: \(\left(\sqrt{3}\right)^x=243\)

=>\(3^{\dfrac{1}{2}\cdot x}=3^5\)

=>\(\dfrac{1}{2}\cdot x=5\)

=>x=10

b: \(0,1^x=1000\)

=>\(\left(\dfrac{1}{10}\right)^x=1000\)

=>\(10^{-x}=10^3\)

=>-x=3

=>x=-3

c: \(\left(0,2\right)^{x+3}< \dfrac{1}{5}\)

=>\(\left(0,2\right)^{x+3}< 0,2\)

=>x+3>1

=>x>-2

d: \(\left(\dfrac{3}{5}\right)^{2x+1}>\left(\dfrac{5}{3}\right)^2\)

=>\(\left(\dfrac{3}{5}\right)^{2x+1}>\left(\dfrac{3}{5}\right)^{-2}\)

=>2x+1<-2

=>2x<-3

=>\(x< -\dfrac{3}{2}\)

e: \(5^{x-1}+5^{x+2}=3\)

=>\(5^x\cdot\dfrac{1}{5}+5^x\cdot25=3\)

=>\(5^x=\dfrac{3}{25,2}=\dfrac{1}{8,4}=\dfrac{10}{84}=\dfrac{5}{42}\)

=>\(x=log_5\left(\dfrac{5}{42}\right)=1-log_542\)