\(\dfrac{1}{32}\) = 2^-5

a) \(15^8\cdot2^4\)

\(=\left(15^2\right)^4\cdot2^4\)

\(=225^4\cdot2^4\)

\(=\left(225\cdot2\right)^4\)

\(=450^4\)

b) \(27^5:32^3\)

\(=\left(3^3\right)^5:\left(2^5\right)^3\)

\(=3^{15}:2^{15}\)

\(=\left(\dfrac{3}{2}\right)^{15}\)

a: \(A=8^2\cdot32^4=2^6\cdot2^{20}=2^{26}\)

b: \(B=27^3\cdot9^4\cdot243=3^9\cdot3^8\cdot3^5=3^{22}\)

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

A = 2 2 . 5 2 - 3 2 - 10 =   81   =   3 4   =   9 2  

\(\begin{array}{l}a){15^8}{.2^4} = {15^{2.4}}{.2^4} = {({15^2})^4}{.2^4}\\ = {225^4}{.2^4} = {(225.2)^4} = {450^4}\\b){27^5}:{32^3} = {({3^3})^5}:{({2^5})^3}\\ = {3^{3.5}}:{2^{5.3}} = {3^{15}}:{2^{15}} = {\left( {\frac{3}{2}} \right)^{15}}\end{array}\)

a) \(15^8\cdot2^4=3^8\cdot5^8\cdot2^4=9^4\cdot25^4\cdot2^4=\left(9\cdot25\cdot2\right)^4=450^4\) 

b) \(27^5:32^3=\left(3^3\right)^5:\left(2^5\right)^3=3^{15}:2^{15}=\left(\dfrac{3}{2}\right)^{15}\)

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

Bài 6: 

a: \(2^{27}=8^9\)

\(3^{18}=9^9\)

b: Vì \(8^9< 9^9\)

nên \(2^{27}< 3^{18}\)

Các số cần tìm là:  4   =   2 2 ;   8   =   2 3 ;   32   =   2 5 ;   81   =   3 4   =   9 2 .