Question

So sánh:

\(\left(\frac{1}{16}\right)^{50}\) và\(\left(\frac{1}{2}\right)^{60}\)

Answer 1

Ta có:

\(\left(\frac{1}{16}\right)^{50}=\left[\left(\frac{1}{2}\right)^4\right]^{50}=\left(\frac{1}{2}\right)^{200}=\frac{1^{200}}{2^{200}}=\frac{1}{2^{200}}\)

\(\left(\frac{1}{2}\right)^{60}=\frac{1^{60}}{2^{60}}=\frac{1}{2^{60}}\)

Vì \(2^{200}>2^{60}\Rightarrow\frac{1}{2^{200}}< \frac{1}{2^{60}}\Rightarrow\left(\frac{1}{16}\right)^{50}< \left(\frac{1}{2}\right)^{60}\)

Answer 2

Ta có:

\(\left(\frac{1}{16}\right)^{50}=\left(\frac{1}{2}\right)^{4.50}=\left(\frac{1}{2}\right)^{200}\)

\(\Rightarrow\left(\frac{1}{2}\right)^{500}>\left(\frac{1}{2}\right)^{60}\)

\(\Rightarrow\left(\frac{1}{16}\right)^{50}>\left(\frac{1}{2}\right)^{60}\)

Answer 3

\(\left(\frac{1}{16}\right)^{50}=\left[\left(\frac{1}{2}\right)^4\right]^{50}=\left(\frac{1}{2}\right)^{200}\)

Vì \(\frac{1}{2}=\frac{1}{2}\) mà \(200>60\)

=> \(\left(\frac{1}{2}\right)^{200}>\left(\frac{1}{2}\right)^{60}\)

=>\(\left(\frac{1}{16}\right)^{50}>\left(\frac{1}{2}\right)^{60}\)

Answer 4

Ta có:\(\left(\frac{1}{16}\right)^{50}=\left[\left(\frac{1}{2}\right)^4\right]^{50}=\left(\frac{1}{2}\right)^{200}\)

Vì \(\left(\frac{1}{2}\right)^{200}< \left(\frac{1}{2}\right)^{60}\) nên \(\left(\frac{1}{16}\right)^{50}< \left(\frac{1}{2}\right)^{60}\)

Answer 5

Ta có\(16^{50}=2^{54}\)

\(2^{54}< 2^{60}\Rightarrow\frac{1}{2^{54}}>\frac{1}{2^{60}}\Rightarrow\left(\frac{1}{16}\right)^{50}>\left(\frac{1}{2}\right)^{60}\)

Answer 6

Pé Jin và Sherlockichi Kudoyle chưa học thuộc ghi nhớ ah:

Số bé hơn 1 càng mũ lên càng bé

Answer 7

\(\left(\frac{1}{16}\right)^{50}=\left(\frac{1}{2}\right)^{200}\)

Rồi bây giờ chỉ cần so sánh số mũ của 2 phân số là đc