Question

So sánh các cặp số sau:

a) 12 mũ 8 & 8 mũ 12

b) (-5) mũ 39 & (-2) mũ 91

Answer 1

a/ Ta có :

\(12^8=\left(12^2\right)^4=24^4\)

\(8^{12}=\left(8^3\right)^4=512^4\)

Vì \(24^4< 512^4\Leftrightarrow12^8< 8^{12}\)

b/ \(\left(-5\right)^{39}=\left[\left(-5\right)^3\right]^{13}=\left(-125\right)^{13}\)

\(\left(-2\right)^{91}=\left[\left(-2\right)^7\right]^{13}=\left(-128\right)^{13}\)

Vì \(\left(-125\right)^{13}>\left(-128\right)^{13}\Leftrightarrow\left(-5\right)^{39}>\left(-2\right)^{91}\)

Answer 2

a)Ta có :

\(12^8=12^{2.4}=\left(12^2\right)^4=144^4\)

\(8^{12}=8^{3.4}=\left(8^3\right)^4=512^4\)

Mà 512>144 nên \(512^4>144^4\)

Vậy \(8^{12}>12^8\)