Bài làm: 

27⁵ : 81³ = 27

10⁶ : 100 = 10000

5⁹ : 25³ = 125

4¹⁰ : 64³ = 4

2²⁵ : 32⁴ = 32

học tốt#

\(27^5:81^3=\left(3^3\right)^5:\left(3^4\right)^3=3^{15}:3^{12}=3^{\left(15-12\right)}=3^3=27\)

\(10^6:100=10^6:10^2=10^{\left(6-2\right)}=10^4=10000\)

\(5^9:25^3=5^9:\left(5^2\right)^3=5^9:5^6=5^{\left(9-6\right)}=5^3=125\)

\(4^{10}:64^3=\left(2^2\right)^{10}:\left(2^6\right)^3=2^{20}:2^{18}=2^{\left(20-18\right)}=2^2=4\)

\(2^{25}:32^4=2^{25}:\left(2^5\right)^4=2^{25}:2^{20}=2^{\left(25-20\right)}=2^5=32\)

\((x-\dfrac{2}{9})^3=(\dfrac{2}{3})^6\)

\(=>(x-\dfrac{2}{9})^3=[(\dfrac{2}{3})^2]^3\)

\(=>(x-\dfrac{2}{9})^3=(\dfrac{4}{9})^3\)

\(=>x-\dfrac{2}{9}=\dfrac{4}{9}\)

\(=>x=\dfrac{4}{9}+\dfrac{2}{9}=\dfrac{2}{3}\)

(x - 2/9)3 = (2/3)6

(x - 2/9)3 = [(2/3²)]³

(x - 2/9)3 = (4/9)³

x - 2/9     = 4/9

x             = 4/9 + 2/9 

x             = 6/9 

x             = 2/3

Vậy x = 2/3 

7^{3 .} 4³ 

= ( 7.4 )³

= 28³

178 : 175

= 17⁸⁺⁵

= 17¹³

\(\left|x-\dfrac{1}{3}\right|+\dfrac{2}{3}=2\dfrac{1}{2}\)

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

\(\Leftrightarrow\left|x-\dfrac{1}{3}\right|=\dfrac{5}{2}-\dfrac{2}{3}\)

\(\Leftrightarrow\left|x-\dfrac{1}{3}\right|=\dfrac{11}{6}\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{3}=\dfrac{-11}{6}\\x-\dfrac{1}{3}=\dfrac{11}{6}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-11}{6}+\dfrac{1}{3}\\x=\dfrac{11}{6}+\dfrac{1}{3}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=\dfrac{13}{6}\end{matrix}\right.\)

\(|x-\dfrac{1}{3}|+\dfrac{2}{3}=2\dfrac{1}{2}\)

\(=>|x-\dfrac{1}{3}|+\dfrac{2}{3}=\dfrac{5}{2}\)

\(=>|x-\dfrac{1}{3}|=\dfrac{5}{2}-\dfrac{2}{3}=\dfrac{11}{6}\)

\(=>\) $\left[\begin{matrix} x-\dfrac{1}{3}=\dfrac{11}{6}\\ x-\dfrac{1}{3}=\dfrac{-11}{6}\end{matrix}\right.$

`=>` $\left[\begin{matrix} x=\dfrac{13}{6}\\ x=\dfrac{-3}{2}\end{matrix}\right.$

\(\left(a^5\right)^7=a^{5.7}=\text{a}^{35}\)

\(\left(a^3\right)^4.a^9=a^{12}.a^9=a^{12+9}=a^{21}\)

\(\left(2^3\right)^5.\left(2^3\right)^4=2^{15}.2^{12}=2^{15+12}=2^{27}\)

( a⁵ ) ⁷ = 5^{5 + 7} = 5^{1 2}

( a ³ ) ⁴ . a⁹ = a^{3 + 4} . a⁹ = a⁷ . a⁹ = a ^{7 +9} = a^{1 6} 

(2³ ) ⁵ . ( 2³ ) ⁴ = 2^{3 + 5} . 2 ^{3 +4} = 2⁸ . 2⁷ = 2^{8 + 7} = 2^{1 5}

a) \(1\dfrac{1}{5}+\dfrac{4}{5}\div x=0,75\)

\(\Leftrightarrow\dfrac{6}{5}+\dfrac{4}{5}\div x=0,75\)

\(\Leftrightarrow\dfrac{4}{5}\div x=\dfrac{-9}{20}\)

\(\Leftrightarrow x=\dfrac{4}{5}\div\dfrac{-9}{20}\)

\(\Leftrightarrow x=-\dfrac{16}{9}\)

b) \(\left|x-\dfrac{1}{3}\right|+\dfrac{2}{3}=2\dfrac{1}{2}\)

\(\Leftrightarrow\left|x-\dfrac{1}{3}\right|=\dfrac{5}{2}-\dfrac{2}{3}\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{3}=\dfrac{11}{6}\\x-\dfrac{1}{3}=\dfrac{-11}{6}\end{matrix}\right.\Leftrightarrow}\left[{}\begin{matrix}x=\dfrac{13}{6}\\x=-\dfrac{3}{2}\end{matrix}\right.\)

đoạn ống nước mới dài số m là:

    0,8+1,35 -\(\dfrac{2}{25}\)= 0,8+ 1,35- 0,08=2.07

Độ dài đoạn ống nước mới là:

Đáp số: $2,07m$

Ta có:

\(\dfrac{a-b}{a+b}=\dfrac{b-c}{b+c}\)

\(=>(a-b)(b+c)=(b-c)(a+b)\)

\(=>ab+ac-b^2-bc=ab+b^2-ac-bc\)

\(=>ab-ab+ac+ac=b^2+b^2-bc+bc\)

\(=>2ac=2b^2\)

\(=>ac=b^2\)

Hay \(b^2=ac\)

     `->Đpcm`

mong mn giúp đỡ