Question

So sánh

a) \(\left(\dfrac{-1}{8}\right)^{25}\) và \(\left(\dfrac{-1}{128}\right)^{13}\)

b) \(32^{30}\) và \(9^{75}\)

Answer 1

a) Có \(\left(\dfrac{-1}{8}\right)^{25}=\left(\dfrac{-1}{2^3}\right)^{25}=\dfrac{-1^{25}}{\left(2^3\right)^{25}}=\dfrac{-1}{2^{75}}\)

\(\left(\dfrac{-1}{128}\right)^{13}=\left(\dfrac{-1}{2^7}\right)^{13}=\dfrac{-1^{13}}{\left(2^7\right)^{13}}=\dfrac{-1}{2^{91}}\)

mà \(\dfrac{1}{2^{75}}>\dfrac{1}{2^{91}}\) <=>\(\dfrac{-1}{2^{75}}< \dfrac{-1}{2^{91}}\)

<=> \(\left(\dfrac{-1}{8}\right)^{25}\) < \(\left(\dfrac{-1}{128}\right)^{13}\)

Answer 2

b) Có 32³⁰ =( 2⁵)³⁰ = 2¹⁵⁰=(2⁶)²⁵=64²⁵

9⁷⁵ = (3³)⁷⁵= 3²²⁵=(3⁹)²⁵=19683²⁵

mà 64²⁵<19683²⁵ <=>32³⁰<9⁷⁵