`@` `\text {Ans}`

`\downarrow`

\(\dfrac{2^8-2^3}{2^5-1}=\dfrac{2^3\left(2^5-1\right)}{2^5-1}=\dfrac{2^3}{1}=2^3=8\)

_____

\(\dfrac{4^8\cdot9^4}{6^6\cdot8^3}\)

`=`\(\dfrac{\left(2^2\right)^8\cdot\left(3^2\right)^4}{2^6\cdot3^6\cdot\left(2^3\right)^3}\)

`=`\(\dfrac{2^{16}\cdot3^8}{2^6\cdot3^6\cdot2^9}\)

`=`\(\dfrac{2^{16}\cdot3^8}{2^{15}\cdot3^6}\)

`=`\(\dfrac{3^2}{2}\) `=`\(\dfrac{9}{2}\)

______

\(\dfrac{27^4\cdot2^3-3^{10}\cdot4^3}{6^4\cdot9^3}\)

`=`\(\dfrac{\left(3^3\right)^4\cdot2^3-3^{10}\cdot\left(2^2\right)^3}{2^4\cdot3^4\cdot\left(3^2\right)^3}\)

`=`\(\dfrac{3^{12}\cdot2^3-3^{10}\cdot2^6}{2^4\cdot3^4\cdot3^6}\)

`=`\(\dfrac{3^{10}\cdot\left(3^2\cdot2^3-2^6\right)}{3^{10}\cdot2^4}\)

`=`\(\dfrac{72-2^6}{2^4}=\dfrac{8}{16}=\dfrac{1}{2}\)

\(\dfrac{2^8-2^3}{2^5-1}=\dfrac{2^3\left(2^5-1\right)}{2^5-1}=2^3=8\)

\(\dfrac{4^8.9^4}{6^6.8^3}=\dfrac{2^{16}.3^8}{2^6.3^6.2^9}=2.3^2=18\)

\(\dfrac{27^4.2^3-3^{10}.4^3}{6^4.9^3}=\dfrac{3^{12}.2^3-3^{10}.2^6}{2^4.3^4.3^6}=\dfrac{2^3.3^{10}.\left(3^2-2^3\right)}{2^4.3^{10}}=\dfrac{9-8}{2}=\dfrac{1}{2}\)

Bài 1 : \(A=1+4+4^2+...+4^{99}\)

\(4A=4+4^2+4^3+...+4^{100}\)

\(4A-A=4^{100}-1\)

\(3A=4^{100}-1\)

Mà \(B=4^{100}\)

\(\Rightarrow3A< B\Leftrightarrow A< \frac{B}{3}\left(ĐPCM\right)\)

1. |15| = 15; |-3| = 3; |0| = 0

2. ko biết vẽ trục số trên đây kiểu j... :v

a) 4³.27 - 4³.23

= 4³.(27-23)

= 4³.4

= 4⁴

b) 35.77+23.35+5³.2³

= 35.(77+23) + (5.2)³

= 35.100 + 10³

= 35.10²+ 10².10

= 10².(35+10)

= 100.45

= 4500

c) 3².5 + 2³.10 - 81 : 3

= 9.5 + 8.2.5 - 27

= 5.(9+8.2) - 27

= 5.25 - 27

= 5³ - 27

= 98

d) 151-2⁹¹:2⁸⁸+1³.3

= 151 - 2³+3

= 151 - 8 + 3

= 146

\(3^2\cdot5+2^3\cdot10-3^4:3\\ =9\cdot5+8\cdot10-3^4\\ =45+80-27\\ =98\)

\(3^2.5+2^3.10-3^4:3\)

\(=9.5+8.10-3^3\)

\(=45+80-27\)

\(=125-27\)

\(=98\)

\(#WendyDang\)

Anh ơi, dòng 2 ( \(3^4:3\) thì ra \(3^3\) -> a mới đổi thành được \(27\) chứ ạ? )

3⁸:3⁴+2²:2³=81,5

3.4²-2.3²=30

(4⁶.3⁴.9³):6¹²=1/9

3⁸:3⁴+2²:2³=3^8-4+2^2-3=3⁴+2^-1=81+0,5=81,5

3.4²-2.3²=3.4²-2.3.3=3.4²-6.3=3.(4²-6)=3.10=30

(4⁶.3⁴.9³):6¹²=(4⁶.3⁴.3⁶):6¹²=(4⁶.3⁴⁺⁶):6¹²=(2¹².3¹⁰):6¹²=\(\frac{2^{12}.3^{10}}{6^{12}}\)=\(\frac{1}{9}\)

=3^8-6+2^2-3=3^2+2^-1=9+0.5=9.5

=3*16-2*9=48-18=30

=(4^6*3^4*9^3)/(3^2*4^6*9^3*3^4)=1/9=\(\frac{1}{9}\)

125*5=5^4

5*25=5^3

=> làm gì có n

a, \(\dfrac{3^8}{3^4}+2^2.2^3\)
= 3⁴ + 2⁵
= 113
b, 3.4² - 2.3²
= 3.(4² - 2.3)
= 3.(16 - 6)
= 3.10
= 30
c, \(\dfrac{4^6.3^4.9^5}{6^{12}}\)

= \(\dfrac{\left(2^2\right)^6.3^4.\left(3^2\right)^5}{\left(2.3\right)^{12}}\)

= \(\dfrac{2^{12}.3^4.3^{10}}{2^{12}.3^{12}}\)

= \(\dfrac{3^{14}}{3^{12}}\)

= 3²
@Dương Tuyết Mai