Question

Hãy so sánh \(\left(\dfrac{1}{63}\right)^7\) và \(\left(\dfrac{1}{16}\right)^{12}\)

Answer 1

\(\left(\dfrac{1}{63}\right)^7=\dfrac{1}{63^7}>\dfrac{1}{64^7}\left(1\right)\)

Ta có: \(\dfrac{1}{64^7}=\dfrac{1}{\left(2^6\right)^7}=\dfrac{1}{2^{42}}\)

\(\left(\dfrac{1}{16}\right)^{12}=\dfrac{1}{16^{12}}=\dfrac{1}{\left(2^4\right)^{12}}=\dfrac{1}{2^{48}}\)

Vì \(2^{42}< 2^{48}\Rightarrow\dfrac{1}{2^{42}}>\dfrac{1}{2^{48}}\left(2\right)\)

Từ \(\left(1\right)và\left(2\right)\) ta suy ra \(\left(\dfrac{1}{63}\right)^7>\left(\dfrac{1}{16}\right)^{12}\)