ta có : \(\left(-\frac{1}{2}\right)^{500}=\left[\left(-\frac{1}{2}\right)^5\right]^{100}=\left(-\frac{1}{32}\right)^{100}\)

=> \(\left(-\frac{1}{16}\right)^{100}< \left(-\frac{1}{32}\right)^{100}\)

<=> \(\left(-\frac{1}{16}\right)^{100}< \left(-\frac{1}{2}\right)^{500}\)

câu b cũng tương tự nha tất cả đưa về cơ số là -2

b)

Ta có: (-32)⁹ = [(-2)⁵]⁹ = (-2)⁴⁵ = (-2)¹³ . 2³²

(-18)¹³ = (-2 . 9)¹³ = (-2)¹³ . (3²)¹³ = (-2)¹³ . 3²⁶

Xét 2³² và 3²⁶:

2³² = (2⁴)⁸ = (2³)⁸ . 2⁸ = 8⁸ . 4⁴

3²⁶ = 9¹³ = 9⁸ . 9⁵

Vì 9⁸ > 8⁸; 9⁵ > 4⁴

=> 9⁸ . 9⁵ > 8⁸ . 4⁴

=> (-2)¹³ . 9⁸ . 9⁵ < (-2)¹³ . 8⁸ . 4⁴

Vậy (-18)³ < (-32)⁹

Còn cách nào khác thì nói nốt ra nha!

a)=         b)<

a) =

b)<

a)=

b)<

k mình nha!!

a) Chỉ cần so sánh \(\left(\frac{1}{16}\right)^{100}\)và \(\left(\frac{1}{2}\right)^{500}\)

Cách 1 : \(\left(\frac{1}{16}\right)^{100}\)= \(\left(\frac{1}{2}\right)^{400}>\left(\frac{1}{2}\right)^{500}\)

Cách 2 : \(\left(\frac{1}{16}\right)^{100}>\left(\frac{1}{32}\right)^{100}=\left(\frac{1}{2}\right)^{500}\)

b) Trước hết ta so sánh : 32⁹ và 18¹³

Ta có : 32⁹ < 2⁴⁵ < 2⁵² = 16¹³ < 18¹³

Vậy -32⁹ > -18¹³ tức là ( -32)⁹ > ( -18)¹³
 

a) \(49^{12}\)và \(5^{40}\)

\(49^{12}=\left(49^3\right)^4=\left(\left(7^2\right)^3\right)^4=\left(7^6\right)^4\)

\(5^{40}=\left(5^{10}\right)^4\)

\(7^6=\left(7^3\right)^2>\left(5^5\right)^2\)vì \(7^2\cdot7>5^3\cdot5^2\)

\(\Rightarrow49^{12}< 5^{40}\)

\(\left(-\frac{1}{16}\right)^{100}=\left(-\left(\frac{-1}{2}\right)^4\right)^{100}\)

\(=\left(-\frac{1}{2}\right)^{400}< \left(-\frac{1}{2}\right)^{500}\)

\(\left(-32\right)^9=-\left(2^5\right)^9=-\left(2^{45}\right)\)

\(\left(-16\right)^{13}=-\left(2^4\right)^{13}=-\left(2^{52}\right)\)

vì -2^45>-2^52hay -16^13>-32^9

\(\text{a) }\left(-\frac{1}{16}\right)^{100}=\frac{\left(-1\right)^{100}}{16^{100}}=\frac{1}{16^{100}}\)

\(\left(-\frac{1}{2}\right)^{500}=\frac{\left(-1\right)^{500}}{2^{500}}=\frac{1}{\left(2^5\right)^{100}}=\frac{1}{32^{100}}\)

Ta co 

\(16^{100}< 32^{100}\)

\(\Rightarrow\frac{1}{16^{100}}>\frac{1}{32^{100}}\)

\(\Rightarrow\left(-\frac{1}{16}\right)^{100}>\left(-\frac{1}{2}\right)^{500}\)

a. 

Ta có:

\(\left(-\frac{1}{16}\right)^{100}=\frac{\left(-1\right)^{100}}{16^{100}}=\frac{1}{16^{100}}\)

\(\left(-\frac{1}{2}\right)^{500}=\frac{\left(-1\right)^{500}}{2^{500}}=\frac{1}{\left(2^5\right)^{100}}=\frac{1}{32^{100}}\)

Vì \(\frac{1}{16^{100}}>\frac{1}{32^{100}}\Rightarrow\left(-\frac{1}{16}\right)^{100}>\left(-\frac{1}{2}\right)^{500}\)

b.

Ta có:

\(\left(-32\right)^9=\left[-\left(2^5\right)\right]^9=-\left(2^{45}\right)\)

\(\left(-16\right)^{13}=\left[-\left(2^4\right)\right]^{13}=-\left(2^{52}\right)\)

Vì \(-\left(2^{45}\right)>-\left(2^{52}\right)\Rightarrow\left(-32\right)^9>\left(-16\right)^{13}\)

#Chúc bạn học tốt!#