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

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!!!

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

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

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

\(d)a\left(-b\right)\left(-a\right)^2\left(-b\right)^3\left(-a\right)^3\left(-b\right)^4\)

\(=\left[a\left(-a\right)^2\left(-a\right)^3\right]\left[\left(-b\right)\left(-b\right)^3\left(-b\right)^4\right]\)

\(=\left[a.a^2\left(-a\right)^3\right]\left[-b.b^4\left(-b\right)^3\right]=\left(-a^3.a^3\right)\left[\left(-b\right)^4.b^4\right]=-b^8\)

\(e)\left[-\left(-a\right)^3\right]\left(-a^2\right)^3\left[\left(-b\right)^2\right]^3\left[-\left(-b\right)^4\right]\)

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

kệ cha nhà bây

a)   378

b)   3

c)    2

d)    2

e)    \(\frac{8748}{1715}\)

Mình thấy bài e) bạn có ghi thiếu ko vậy.81^2 x;: hay là cộng trừ vậy?

3^12.(3^4)^11/(3^3)^10.(3^2)^15=3^12.3^44/3^30.3^30=3^56/3^30

=3^17.9^22/3^30.9^15=9^7/3^13=3^14/3^13=3^1=3

giùm nhé bạn

a/\(378\)

b/\(3\)

3¹⁷.81¹¹/27¹⁰.9¹⁵

=3¹⁷.(3⁴)¹¹/(3³)¹⁰.(3²)¹⁵

=3¹⁷.3⁴⁴/3³⁰.3³⁰

=3⁶¹/3⁶⁰

=3

\(\frac{3^{17}.81^{11}}{27^{10}.9^{15}}=\frac{3^{17}.\left(3^4\right)^{11}}{\left(3^3\right)^{10}.\left(3^2\right)^{15}}=\frac{3^{17}.3^{41}}{3^{30}.3^{30}}=\frac{3^{17+41}}{3^{30+30}}=\frac{3^{58}}{3^{60}}=\frac{1}{3^2}=\frac{1}{9}\)

nho k day