Question

Answer 1

Mình làm mẫu vài câu các câu khác tương tự nha .

\(a,4^{10}.8^{15}=\left(2^2\right)^{10}.\left(2^3\right)^{15}=2^{20}.2^{45}=2^{20+45}=2^{65}\)

\(c,27^{19}:9^{10}=\left(3^3\right)^{19}:\left(3^2\right)^{10}=3^{57}:3^{20}=3^{57-20}=3^{37}\)

\(d,\dfrac{2^{10}.13+2^{10}.65}{2^8.10^4}=\dfrac{2^{10}.78}{2^8.10^4}=\dfrac{2^2.78}{10^4}=\dfrac{2^3.39}{2^4.5^4}=\dfrac{39}{2.5^4}=\dfrac{39}{1250}\)

\(h,\left(1+2+3+...+100\right)\left(1^2+...+10^2\right)\left(65.111-13.15.37\right)\)

\(=\left(1+2+3+...+100\right)\left(1^2+...+10^2\right)\left(5.13.3.37-13.15.37\right)\)

\(=\left(1+2+3+...+100\right)\left(1^2+...+10^2\right)\left(15.13.37-13.15.37\right)\)

\(=\left(1+2+3+...+100\right)\left(1^2+...+10^2\right).0=0\)

Answer 2

a,4¹⁰.8¹⁵ = (2²)¹⁰.(2³)¹⁵ = 2²⁰.2⁴⁵ = 2⁶⁵

b,4¹⁵.5³⁰ = 4¹⁵.(5²)¹⁵ = 4¹⁵.25¹⁵ = (4.25)¹⁵ = 100¹⁵ 

c, 27¹⁹:9¹⁰ = (3³)¹⁹:(3²)¹⁰ = 3⁵⁷:3²⁰ = 3³⁷

d, \(\dfrac{72^3.54^2}{108^4}=\dfrac{\left(2^3.3^2\right)^3.\left(3^3.2\right)^2}{\left(2^2.3^3\right)^4}=\dfrac{2^9.3^6.3^6.2^2}{2^8.3^{12}}=2.2^2\)\(=2.4=8\)

Answer 3

Giải:

a) \(4^{10}.8^{15}=\left(2^2\right)^{10}.\left(2^3\right)^{15}=2^{20}.2^{45}=2^{65}\) 

b) \(4^{15}.5^{30}=\left(2^2\right)^{15}.5^{30}=2^{30}.5^{30}=\left(2.5\right)^{30}=10^{30}\) 

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

d) \(\dfrac{72^3.54^2}{108^4}=\dfrac{\left(8.9\right)^3.\left(6.9\right)^2}{\left(9.12\right)^4}=\dfrac{2^9.9^3.2^2.3^2.9^2}{9^4.3^4.2^8}=\dfrac{2^{11}.9^5.3^2}{9^4.3^4.2^8}=\dfrac{2^3.9}{3^2}=\dfrac{8.9}{9}=8\) 

e) \(\dfrac{3^{10}.11+3^{10}.5}{3^9.2^4}=\dfrac{3^{10}.\left(11+5\right)}{3^9.2^4}=\dfrac{3.16}{16}=3\) 

g) \(\dfrac{2^{10}.13+2^{10}.65}{2^8.10^4}=\dfrac{2^{10}.\left(13+65\right)}{2^8.10^4}=\dfrac{2^2.78}{2^4.5^4}=\dfrac{2^2.2.39}{2^4.5^4}=\dfrac{2^3.39}{2^4.625}=\dfrac{39}{2.625}=\dfrac{39}{1250}\) 

h) \(\left(1+2+3+...+100\right).\left(1^2+2^3+3^2+...+10^2\right).\left(65.111-13.15.37\right)\) 

\(=\left(1+2+3+...+100\right).\left(1^2+2^3+3^2+...+10^2\right).\left(65.111-13.5.3.37\right)\) 

\(=\left(1+2+3+...+100\right).\left(1^2+2^3+3^2+...+10^2\right).\left(65.111-65.111\right)\) 

\(=\left(1+2+3+...+100\right).\left(1^2+2^3+3^2+...+10^2\right).0\) 

\(=0\)

Chúc bạn học tốt!