Question

So sánh:

(1/27)mũ 10 và (1/81)mũ 7

Answer 1

\(\left(\dfrac{1}{27}\right)^{10}=\dfrac{1}{27^{10}}=\dfrac{1}{\left(3^3\right)^{10}}=\dfrac{1}{3^{30}}\)

\(\left(\dfrac{1}{81}\right)^7=\dfrac{1}{81^7}=\dfrac{1}{\left(3^4\right)^7}=\dfrac{1}{3^{28}}\)

Do \(3^{30}>3^{28}\Leftrightarrow\dfrac{1}{3^{30}}< \dfrac{1}{3^{28}}\)

\(\Leftrightarrow\left(\dfrac{1}{27}\right)^{10}< \left(\dfrac{1}{81}\right)^7\)

Answer 2

Ta có:

\(\left(\dfrac{1}{27}\right)^{10}=\left(\dfrac{1}{3^3}\right)^{10}=\left(\dfrac{1}{3}\right)^{30}\)

\(\left(\dfrac{1}{81}\right)^7=\left(\dfrac{1}{3^5}\right)^7=\left(\dfrac{1}{3}\right)^{35}\)

Vì \(\left(\dfrac{1}{3}\right)^{35}>\left(\dfrac{1}{3}\right)^{30}\)

⇒\(\left(\dfrac{1}{27}\right)^{10}< \left(\dfrac{1}{81}\right)^7\)