Giúp mik với
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. \(a\left(-b\right)\left(-a\right)^2\left(-b\right)^3\left(-a\right)^3\left(-b\right)^4\)
e. \([-\left(-a\right)^3]\left(-a^2\right)^3.[\left(-b\right)^2]^3.[-\left(-b\right)^4]\)
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) \(\frac{9^2.2^{11}}{16^2.6^3}=\frac{\left(3^2\right)^2.2^{11}}{\left(2^4\right)^2.2^3.3^3}=\frac{3^4.2^{11}}{2^8.2^3.3^3}=\frac{3^4.2^{11}}{2^{11}.3^3}=3\)
c) \(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{31}+2^{41}.3^6}=\frac{2^{10}.3^{31}+2^{40}.3^6}{2.\left(2^{10}.3^{31}+2^{40}.3^6\right)}=\frac{1}{2}\)
Các bạn vào trang cá nhân của mik đi, có cái này hay lắm!!!
\(a)\frac{3^{17}.81^{11}}{27^{10}.9^{15}}=\frac{3^{17}.\left(3^4\right)^{11}}{\left(3^3\right)^{10}.\left(3^2\right)^{15}}=\frac{3^{17}.3^{44}}{3^{30}.3^{30}}=\frac{3^{61}}{3^{60}}=3\)
\(b)\frac{9^2.2^{11}}{16^2.6^3}=\frac{\left(3^2\right)^2.2^{11}}{\left(2^4\right)^2.2^3.3^3}=\frac{3^4.2^{11}}{2^{11}.3^3}=3\)
\(c)\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{31}+2^{41}.3^6}=\frac{2^{10}.3^6\left(3^{25}+2^{30}\right)}{2^{11}.3^6\left(3^{25}+2^{30}\right)}=\frac{1}{2}\)
\(d)a\left(-b\right)\left(-a\right)^2\left(-b\right)^3\left(-a\right)^3\left(-b\right)^4\)
\(=\left[a\left(-a\right)^2\left(-a\right)^3\right]\left[\left(-b\right)\left(-b\right)^3\left(-b\right)^4\right]\)
\(=\left[a.a^2\left(-a\right)^3\right]\left[-b.b^4\left(-b\right)^3\right]=\left(-a^3.a^3\right)\left[\left(-b\right)^4.b^4\right]=-b^8\)
\(e)\left[-\left(-a\right)^3\right]\left(-a^2\right)^3\left[\left(-b\right)^2\right]^3\left[-\left(-b\right)^4\right]\)
\(=a^3\left(-a^6\right).b^6\left(-b^4\right)=-a^3.\left(-b^2\right)=a^3b^2\)
