\(27\cdot5^3\cdot3^3\cdot32^{-1}:125=3^3\cdot5^3\cdot3^3\cdot\dfrac{1}{32}:5^3=\dfrac{3^6}{32}=\dfrac{3^6}{2^5}\)

125=5³=

-125=(-5)³

27=3³

-27=(-3)³

125 =5³ - 125=(-5)³ ; 27 =3³; - 27 =(-3)³

1=1^2 ;125=5^3 ;-125=-5^3; 27=27^1; -27= -27^1

2: 5^2 25^1 

a) \(\left(\frac{1}{16}\right)^{25}\div\left(\frac{1}{2}\right)^{30}=\left(\frac{1}{2^4}\right)^{25}\div\left(\frac{1}{2}\right)^{30}=\left[\left(\frac{1}{2}\right)^4\right]^{25}\div\left(\frac{1}{2}\right)^{30}=\left(\frac{1}{2}\right)^{4.25}\div\left(\frac{1}{2}\right)^{30}\)

\(=\left(\frac{1}{2}\right)^{100}\div\left(\frac{1}{2}\right)^{30}=\left(\frac{1}{2}\right)^{100-30}=\left(\frac{1}{2}\right)^{70}\)

b) \(584^{100}\div292^{100}=\left(584-292\right)^{100}=292^{100}\)

c) \(125^4\cdot16^3=\left(5^3\right)^4\cdot\left(2^4\right)^3=5^{3\cdot4}\cdot2^{4\cdot3}=5^{12}\cdot2^{12}=\left(5+2\right)^{12}=7^{12}\)

1/81 = (1/9)^2

243 = 3^5

8. 3^3 = 2^3 . 3^3 = 6^3 

81.2^8 = 9^2 . (2^4)^2 = 9^2 . 16^2 = ( 9. 16)^2 =  144^2  

\(125=5^3\)

\(-125=\left(-5\right)^3\)

\(27=3^3\)

\(-27=\left(-3\right)^3\)

 ^...^ ^_^

Bài 11: Viết các số sau dưới dạng lũy thừa với số mũ khác 1:

125 = 5³

(-125) = (-5)³

27 = 3³

(-27) = (-3)³

125 = 125^2-1 ; - 125 = - 125^1009-1008 ; 27 = 27^{10000000000-9999999999} ; - 27 = - 27^{\(\infty+1-\infty\)}             :)

a) \(8=2^3\)

\(16=4^2\)

\(27=3^3\)

\(81=9^2\)

\(100=10^2\)

b) \(1000=10^3\)

\(1,000,000=10^6\)

\(1,000,000,000=10^9\)

100.000 } 12 chữ số 0 = 10^12