Question

Tính giá trị của các biểu thức :
a) \(\frac{3^{17}.81^{11}}{27^{10}.9^{15}}\)
b) \(\frac{9^2.2^{11}}{16^2.6^3}\)
c) \(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{31}+2^{41}.3^6}\)
d) a.(-b)(-a)²(-b)³(-a)³(-b)⁴

e) [ - ( -a)³ ] (-a²)³.[ ( -b)² ]³ . [ - ( -b)⁴ ]
 

Answer 1

a)  \(\frac{3^{17}.81^{11}}{27^{10}.9^{15}}=\frac{3^{17}.\left(3^4\right)^{11}}{\left(3^3\right)^{10}.\left(3^2\right)^{15}}=\frac{3^{17}.3^{44}}{3^{30}.3^{30}}=\frac{3^{61}}{3^{60}}=3\)

b)  \(\frac{9^2.2^{11}}{16^2.6^3}=\frac{\left(3^2\right)^2.2^{11}}{\left(2^4\right)^2.\left(2.3\right)^3}=\frac{3^4.2^{11}}{2^8.2^3.3^3}=3\)

c)  \(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{31}+2^{41}.3^6}=\frac{2^{10}.3^6.\left(3^{25}+2^{30}\right)}{2^{11}.3^6.\left(3^{25}+2^{30}\right)}=\frac{1}{2}\)

d)  \(a.\left(-b\right).\left(-a\right)^2\left(-b\right)^3.\left(-a\right)^3.\left(-b\right)^4=-a^6b^8\)