Question

So sánh:   \(\left(-\frac{1}{8}\right)^{180}\) và \(\left(-\frac{1}{4}\right)^{200}\)

Answer 1

bằng nhau

Answer 2

ta có:\(\left(-\frac{1}{8}\right)^{180}=\left(\frac{1}{8}\right)^{180}=\left(\frac{1}{4}\right)^{2^{180}}=\left(\frac{1}{4}\right)^{360}\) 

ta có :\(\left(-\frac{1}{4}\right)^{200}=\left(\frac{1}{4}\right)^{200}\)

=>(1/4)^360<(1/4)^200

Vậy : (-1/8)^180 < ( -1/4)^200

Answer 3

Ta có: \(\left(\frac{-1}{8}\right)^{180}=\frac{-1^{180}}{8^{180}}=\frac{1}{8^{180}}\)

\(\left(\frac{-1}{4}\right)^{200}=\frac{-1^{200}}{4^{200}}=\frac{1}{4^{200}}\)

Suy ra để so sánh \(\left(\frac{-1}{8}\right)^{180}\)và\(\left(\frac{-1}{4}\right)^{200}\)thì ta chỉ cần so sánh 8¹⁸⁰ và 4²⁰⁰

Ta có: 8¹⁸⁰=(2³)¹⁸⁰=2^3.180=2⁵⁴⁰

             4²⁰⁰=(2²)²⁰⁰=2^2.200=2⁴⁰⁰

       Ta thấy 2=2 nhưng 540>400 suy ra 8¹⁸⁰>4²⁰⁰ suy ra \(\frac{1}{8^{180}}< \frac{1}{4^{200}}\)suy ra \(\left(\frac{-1}{8}\right)^{180}< \left(\frac{-1}{4}\right)^{200}\)

Answer 4

Ta có:\(\left(\frac{-1}{8}\right)^{180}\)\(=\frac{-1^{180}}{8^{180}}\)\(=\frac{1}{8^{180}}\)\(=\frac{1}{\left(4.2\right)^{180}}\)\(=\frac{1}{4^{180}}\cdot\frac{1}{2^{180}}\)\(=\frac{1}{4^{180}}\cdot\frac{1}{4^{90}}\)

          \(\left(\frac{-1}{4}\right)^{200}\)\(=\frac{-1^{200}}{4^{200}}\)\(=\frac{1}{4^{200}}\)\(=\frac{1}{4^{180}}\cdot\frac{1}{4^{20}}\)

            Vì1/4^90>1/4^20 \(\Rightarrow\)1/4^180*1/4^90<1/4^180*1/4^20 Hay (-1/8)^180<(-1/4)^200

Dưới mỏi tay nên vt vậy khi viết nhớ vt lại nha