Question

so sanh

a) \(\left(\frac{1}{16}\right)^{200}\)va\(\left(\frac{1}{2}\right)^{1000}\)

b) (-32)²⁷ va (-18)³⁹

Answer 1

a, Có : (1/60)^200 = [(1/2)^4]^200 = (1/2)^800

Vì 0 < 1/2 < 1 nên (1/2)^800 > (1/2)^1000

=> (1/16)^200 > (1/2)^1000

Tk mk nha

Answer 2

a) \(\left(\frac{1}{16}\right)^{200}=\left(\frac{1}{2}\right)^{800}< \left(\frac{1}{2}\right)^{1000}\)

Answer 3

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

\(\left(\frac{1}{2}\right)^{1000}=\frac{1}{2^{1000}}\)

có : \(16^{200}=\left(2^4\right)^{200}=2^{800}\)

ta thấy \(2^{800}< 2^{1000}\)

\(\Rightarrow16^{200}< 2^{1000}\)

\(\Rightarrow\frac{1}{16^{200}}>\frac{1}{2^{1000}}\)

\(\Rightarrow\left(\frac{1}{16}\right)^{200}>\left(\frac{1}{2}\right)^{100}\)

Answer 4

a)   Ta có: \(\left(\frac{1}{16}\right)^{200}=\frac{1}{\left(16\right)^{200}}=\frac{1}{\left(2^4\right)^{200}}=\frac{1}{2^{800}}=\left(\frac{1}{2}\right)^{800}>\left(\frac{1}{2}\right)^{1000}\)

b)   Ta có:  \(32^{27}=\left(2^5\right)^{27}=2^{135}< 2^{156}=\left(2^4\right)^{39}=16^{39}< 18^{39}\)

\(\Rightarrow\left(-32\right)^{27}>\left(-18\right)^{39}\)( Do chuyển từ âm sang dương )