câu c là (2\(^2\))\(^3\)và 2 mũ 2 mũ 3 nha

giúp mk nhanh 1 chút mk cần rất rất gấp

\(a,2^{24}=\left(2^3\right)^8=8^8< 9^8=\left(3^2\right)^8=3^{16}\\ b,16^{11}=\left(2^4\right)^{11}=2^{44}< 2^{45}=\left(2^5\right)^9=32^9\\ \Rightarrow\left(-16\right)^{11}>\left(-32\right)^9\\ c,\left(2^2\right)^3=2^6< 2^8=2^{2^3}\)

(-23)^9 < (-16)^3

(-32)^9<(-16)^3 vì

(-32)^9= ((-2)^5)^9= (-2)^45

(-16)^3= ((-2)^4)^3= (-2)^12

Vì (-2)^45<(-2)^12=> (-32)^9<(-16)^3

\(\left(-32\right)^9=\left(-2^5\right)^9=\left(-2\right)^{45}\)

\(\left(-16\right)^3=\left(-2^4\right)^3=\left(-2\right)^{12}=2^{12}>-2^{45}\)

\(\Rightarrow\left(-16\right)^3>\left(-32\right)^9\)

b,                                                     Bài giải

\(\left(-32\right)^9=\left(-16\cdot2\right)^9=\left(-16\right)^9\cdot2^9\)

\(\left(-16\right)^{13}=\left(-16\right)^9\cdot\left(-16\right)^4=\left(-16\right)^9\cdot\left[\left(-2\right)^4\right]^4=\left(-16\right)^9\cdot\left(-2\right)^{16}=\left(-16\right)^9\cdot2^{16}\)

Vì \(2^9< 2^{16}\) nên \(\left(-32\right)^9>\left(-16\right)^{13}\)

a) \(32^{50}\)và \(27^{51}\)

\(32^{50}=\left(32^2\right)^{25}=1024^{25}\)

\(27^{51}=\left(27^2\right)^{25}.27=729^{25}.27\)

Vì \(1024>729\)nên \(1024^{25}>729^{25}.27\)hay \(32^{50}>27^{51}\)

b) \(31^9\)và \(9^{16}\)

\(31^9=\left(91^3\right)^2=273^2\)

\(9^{16}=\left(9^2\right)^4=81^4=\left(81^2\right)^2=6561^2\)

Vì \(6561>273\)nên \(273^2< 6561^2\)hay \(31^9< 9^{16}\).

ta có (-32)^9=(-2)^5)^9=(-2)^45

          (16)^11=(2^4)^11=2^44

Vì -2<2 suy ra (-2)^45<2^44 suy ra 16^11>(-32)^9

Đây nhé bn :))