a)4¹⁰. 8¹⁵ = (2²)¹⁰.(2³)¹⁵
                    =2²⁰.2⁴⁵
                 =2⁶⁵
b) 4¹⁵ . 5³⁰ =  4¹⁵ . (5²)¹⁵
                   = 4¹⁵ . 25¹⁵
                   =  (4.25)¹⁵ 
                   = 100¹⁵
c) 27¹⁶ : 9¹⁰ = (3³)¹⁶ : (3²)¹⁰
                     =3⁴⁸ : 3²⁰
                         =328
d)A=\(\frac{72^3.54^2}{108^4}\)

TS:72³.54²=(2.2.2.3.3)³.(2.3.3.3)²
                      =2³.2³.2³.3³.3³.2².3².3².3²
                      =2^3+3+3+2.3^3+3+2+2+2
                      =2¹¹.3¹²
MS:108⁴=(2.2.3.3.3)⁴
               =2⁴. 2⁴.3⁴.3⁴.3⁴
               =2⁴⁺⁴ . 3⁴⁺⁴⁺⁴
               =2⁸ . 3¹²
\(\Rightarrow\)A=\(\frac{2^{11}.3^{12}}{2^8.3^{12}}\) = 2³=8
e)B=\(\frac{3^{10}.11+3^{10}.5}{3^9.2^4}\)
TS:3¹⁰ .11 + 3¹⁰ .5 = 3¹⁰ . (11+5)
                               = 3¹⁰ .  16
                               = 3¹⁰. 2⁴
\(\Rightarrow\)B=\(\frac{3^{10}.2^4}{3^9.2^4}\) = 3¹=3

a, \(B=\dfrac{2^{10}.13+2^{10}.65}{2^8.104}\)

\(=\dfrac{2^{10}.\left(13+65\right)}{2^8.2^3.13}\)

\(=\dfrac{2^{10}.78}{2^{11}.13}\)\(=\dfrac{1.6}{2.1}=\dfrac{1.3}{1.1}=3\)

b: \(=\dfrac{2^{20}\cdot3^2+2^{54}}{2^{18}\cdot5^2}=\dfrac{2^{20}\left(3^2+2^{32}\right)}{2^{18}\cdot5^2}=\dfrac{2^2\left(3^2+2^{32}\right)}{25}\)

c: \(=\dfrac{2^9\cdot3^6\cdot3^6\cdot2^2}{2^8\cdot3^{12}}=\dfrac{2^{11}}{2^8}=8\)

d: \(=\dfrac{2^{12}\cdot3^4\cdot3^{10}}{2^{12}\cdot3^{12}}=9\)

a, A = \(\frac{2^{10}.13+2^{10}.65}{2^8.104}\)

\(A=\frac{2^{10}\left(13+65\right)}{2^8.2^2.26}=\frac{2^{10}.78}{2^{10}.26}=\frac{78}{26}=3\)

Vậy A = 3

b, \(B=\frac{72^3.54^2}{108^4}=\frac{72^3.54^2}{\left(54.2\right)^4}=\frac{72^3.54^2}{54^4.2^4}=\frac{72^3}{54^2.2^4}=\frac{\left(8.9\right)^3}{\left(6.9\right)^2.2^4}\)

\(=\frac{\left(2^3\right)^3.9^3}{6^2.9^2.2^4}=\frac{2^9.9^3}{2^2.3^2.9^2.2^4}=\frac{2^9.9^3}{2^6.9^3}=\frac{2^9}{2^6}=2^3=8\)

Vậy B = 8

c, \(C=\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}=\frac{11.3^{29}.3^{30}}{2^2.3^{28}}=\frac{11.3^{29}.3.3^{29}}{2^2.3^{28}}=\frac{\left(11-3\right)3^{29}}{2^2.3^{28}}\)

\(=\frac{2^3.3^{29}}{2^2.3^{28}}=2.3=6\)

Vậy C = 6

d, \(D=\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}=\frac{\left(3.2^{18}\right)^2}{11.2^{35}-\left(2^4\right)^9}=\frac{3^2.2^{36}}{11.2^{35}-2^{36}}=\frac{3^2.2^{36}}{\left(11-2\right)2^{35}}=\frac{3^2.2}{9}=2\)

Vậy D = 2

\(A=\dfrac{3^{10}\cdot11+3^{10}\cdot5}{3^9\cdot2^4}=\dfrac{3^{10}\cdot\left(11+5\right)}{3^9\cdot16}=\dfrac{3^{10}\cdot16}{3^9\cdot16}=3\)

\(B=\dfrac{2^{10}\cdot13+2^{10}\cdot65}{2^8\cdot104}=\dfrac{2^{10}\cdot\left(13+65\right)}{2^8\cdot2^2\cdot26}=\dfrac{2^{10}\cdot78}{2^{10}\cdot26}=3\)

\(C=\dfrac{72^3\cdot54^2}{108^4}=\dfrac{\left(2^3\cdot3^2\right)^3\cdot\left(2\cdot3^3\right)^2}{\left(3^3\cdot2^2\right)^4}\\ =\dfrac{2^9\cdot3^6\cdot2^4\cdot3^6}{3^{12}\cdot2^8}=\dfrac{2^{13}\cdot3^{12}}{3^{12}\cdot2^8}=2^5=32\)

\(D=\dfrac{11\cdot3^{22}\cdot3^7-9^{15}}{\left(2\cdot3^{14}\right)^2}=\dfrac{11\cdot3^{29}-\left(3^2\right)^{15}}{2^2\cdot3^{28}}=\dfrac{11\cdot3^{29}-3^{30}}{2^2\cdot3^{28}}\\ =\dfrac{3^{29}\cdot\left(11-3\right)}{2^2\cdot3^{28}}=\dfrac{3^{29}\cdot8}{4\cdot3^{28}}=3\cdot2=6\)

Gợi ý 

bn thực hiện phép tính tử mẫu bình thường , khi ra nhưng số trùng nhau bn gạch ra nháp cho đến nhưng số tối giản là ra nha 

chúc bn

học tốt

A = \(\frac{3^{10}.11+3^{10}.5}{3^9.2^4}\)

  = \(\frac{3^{10}\left(11+5\right)}{3^9.2^4}\)

 = \(\frac{3^{10}.16}{3^9.2^4}\)

 = \(\frac{3^{10}.2^4}{3^9.2^4}=3\)

B = \(\frac{2^{10}.13+2^{10}.65}{2^8.104}\)

  = \(\frac{2^{10}\left(13+65\right)}{2^8.104}\)

  = \(\frac{2^{10}.78}{2^8.104}\)

  = \(\frac{2^{10}.13.2.3}{2^8.2^3.13}\)

 = \(\frac{2^{11}.13.3}{2^{11}.13}=3\)

C = \(\frac{72^3.54^2}{108^4}\)

  = \(\frac{\left(2^3.3^2\right)^3.\left(2.3^3\right)^2}{\left(2^2.3^3\right)^4}\)

  = \(\frac{2^9.3^6.2^2.3^6}{2^8.3^{12}}\)

 = \(\frac{2^{11}.3^{12}}{2^8.3^{12}}\)

= \(2^3=8\)

\(A=\frac{3^{10}.11+3^{10}.5}{3^9.2^4}=\frac{3^{10}.16}{3^9.16}=3\)

\(B=\frac{2^{10}.13+2^{10}.65}{2^8.104}=\frac{2^{10}.78}{2^8.104}=\frac{2^{10}.26.3}{2^8.2^2.26}=3\)

\(C=\frac{72^3.52^4}{108^4}=\frac{\left(3^2.2^3\right)^3.\left(13.2^2\right)^4}{\left(3^3.2^2\right)^4}=\frac{3^6.2^9.13^4.2^8}{3^{12}.2^8}=\frac{2^9.13^4}{3^6}\)

\(D=\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}=\frac{11.3^{29}-\left(3^2\right)^{15}}{2^2.3^{28}}=\frac{11.3^{29}-3^{30}}{2^2.3^{28}}=\frac{3^{29}\left(33-1\right)}{2^2.3^{28}}=\frac{3^{29}.2^5}{2^2.3^{28}}=3.8=24\)