Để giải bài toán này, chúng ta sẽ tính từng phần và sau đó kết hợp kết quả cuối cùng.

72^3 = 72 * 72 * 72 = 373248 54^2 = 54 * 54 = 2916 108^4 = 108 * 108 * 108 * 108 = 16777216

Bây giờ, ta thay các giá trị này vào biểu thức:

(72^3 * 54^2) / 108^4 = (373248 * 2916) / 16777216

Tiếp theo, ta thực hiện phép tính trong ngoặc, sau đó chia cho 16777216:

(373248 * 2916) / 16777216 = 1088391168 / 16777216

Kết quả là 64.8.

Vậy, giá trị của biểu thức là 64.8.

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

\(=\dfrac{2^{11}\cdot3^{12}}{2^8\cdot3^{12}}=2^3=8\)

\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+...+\frac{89}{90}\)

\(=1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+...+1-\frac{1}{90}\)

\(=9-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\)

\(=9-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)

\(=9-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{9}-\frac{1}{10}\right)\)

\(=9-\left(1-\frac{1}{10}\right)\)

\(=9-\frac{9}{10}=\frac{81}{10}\)

a.

\(4^{10}\times8^{15}=\left(2^2\right)^{10}\times\left(2^3\right)^{15}=2^{20}\times2^{45}=2^{65}\)

b.

\(4^{15}\times5^{30}=\left(2^2\right)^{15}\times5^{30}=2^{30}\times5^{30}=\left(2\times5\right)^{30}=10^{30}\)

c.

\(\frac{27^{16}}{9^{10}}=\frac{\left(3^3\right)^{16}}{\left(3^2\right)^{10}}=\frac{3^{48}}{3^{20}}=3^{28}\)

d.

\(A=\frac{72^3\times54^2}{108^4}=\frac{\left(8\times9\right)^3\times\left(27\times2\right)^2}{\left(27\times4\right)^4}=\frac{\left(2^3\times3^2\right)^3\times\left(3^3\times2\right)^2}{\left(3^3\times2^2\right)^4}=\frac{2^9\times3^6\times3^6\times2^2}{3^{12}\times2^8}=2^3=8\)

e.

\(B=\frac{3^{10}\times11+3^{10}\times5}{3^9\times2^4}=\frac{3^{10}\times\left(11+5\right)}{3^9\times16}=\frac{3\times16}{16}=3\)

Chúc bạn học tốt

a=???????????????????????????

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, \(A=\dfrac{3^{10}.11+3^{10}.5}{3^9.2^4}=\dfrac{3^{10}.\left(11+5\right)}{3^9.2^4}\)

\(=\dfrac{3^{10}.2^4}{3^9.2^4}=3\)

b, \(B=\dfrac{2^{10}.13+2^{10}.65}{2^8.104}=\dfrac{2^{10}.78}{2^8.104}\)

\(=\dfrac{2^2.3}{4}=3\)

c, \(C=\dfrac{4^9.36+64^4}{16^4.100}=\dfrac{\left(2^2\right)^9.36+\left(2^6\right)^4}{\left(2^4\right)^4.100}\)

\(=\dfrac{2^{18}.36+2^{24}}{2^{16}.100}=\dfrac{2^{18}.\left(36+2^6\right)}{2^{16}.100}\)

\(=\dfrac{2^4.100}{100}=2^4=16\)

Câu d làm tương tự! Chúc bạn học tốt!!!

d, \(D=\dfrac{72^3.54^2}{108^4}=\dfrac{\left(2^3.3^2\right)^3.\left(2.3^3\right)^2}{\left(2^2.3^3\right)^4}\)

\(=\dfrac{2^9.3^6.2^2.3^6}{2^8.3^{12}}=2^3=8\)

Chúc bạn học tốt!!!

\(a=\dfrac{3^{10}.11+3^{10}.5}{3^9.2^4}=\dfrac{3^{10}\left(11+5\right)}{3^9.16}=\dfrac{3^{10}.16}{3^9.16}=\dfrac{3^{10}}{3^9}=3\)

\(b=\dfrac{2^{10}.13+2^{10}.65}{2^8.104}=\dfrac{2^{10}\left(13+65\right)}{2^8.2^2.26}=\dfrac{2^{10}.78}{2^{10}.26}=\dfrac{78}{26}=3\)

\(c=\dfrac{4^9.36+64^4}{16^4.100}=\dfrac{4^9.36+\left(4^3\right)^4}{\left(4^2\right)^4.100}=\dfrac{4^9.36+4^{12}}{4^8.100}=\dfrac{4^9.36+4^9.4^3}{4^8.100}=\dfrac{4^9.36+4^9.64}{4^8.100}=\dfrac{4^9\left(36+64\right)}{4^8.100}=\dfrac{4^9.100}{4^8.100}=\dfrac{4^9}{4^8}=4\)

\(d=\dfrac{72^3.54^2}{108^4}=\dfrac{\left(2^3.3^2\right)^3.\left(2.3^3\right)^2}{\left(2^2.3^3\right)^4}=\dfrac{2^9.3^6.2^2.3^6}{2^8.3^{12}}=\dfrac{2^{11}.3^{12}}{2^8.3^{12}}=\dfrac{2^{11}}{2^8}=2^3=8\)