`(1/243)^9 = [1/(3^5)]^9 = [(1/3)^5]^9=(1/3)^13`

Vì: `1/3 > 1/83`

`=> (1/3)^13 > 1/(83)^13`.

\(\left(\frac{1}{243}\right)^9=\frac{1}{243^9}=\frac{1}{\left(3^5\right)^9}=\frac{1}{3^{45}}\)

\(\left(\frac{1}{83}\right)^{13}< \left(\frac{1}{81}\right)^{13}=\frac{1}{81^{13}}=\frac{1}{\left(3^4\right)^{13}}=\frac{1}{3^{52}}\)

Có \(3^{45}< 3^{52}\Rightarrow\frac{1}{3^{45}}>\frac{1}{3^{52}}\)

suy ra \(\left(\frac{1}{243}\right)^9>\left(\frac{1}{83}\right)^{13}\).

\(\left(\frac{1}{243}\right)^9=\left(\frac{1}{3^4}\right)^9=\frac{1}{3^{4.9}}=\frac{1}{3^{36}}\)

\(\left(\frac{1}{83}\right)^{13}\frac{1}{3^{42}}\Rightarrow\left(\frac{1}{81}\right)^{13}

Ta có : 

\(\frac{1}{243^9}=\frac{1}{\left(81.3\right)^9}=\frac{1}{81^9.27^3}>\frac{1}{81^9.81^3}=\frac{1}{81^{11}}>\frac{1}{8^{12}}>\frac{1}{8^{13}}\)

\(\Rightarrow\frac{1}{243^9}>\frac{1}{8^{13}}\)

Ta có :

\(\frac{1}{243^9}=\frac{1}{\left(81.3\right)^9}=\frac{1}{81^9.27^3}>\frac{1}{81^9.81^3}=\frac{1}{81^{11}}>\frac{1}{8^{12}}>\frac{1}{8^{13}}\)

\(\Rightarrow\frac{1}{243^9}>\frac{1}{83^{13}}\)

mình chắc chắn luôn

-https://olm.vn/hoi-dap/detail/77727486175.html

a, <

b, <

c, >

d, >

bn làm chi tiết nhé!!!!!!!!!!!!!!!!!!!!!!!!!!

a) \(\left(\frac{1}{243}\right)^9=\left(\frac{1}{3^5}\right)^9=\frac{1}{3^{45}}\)

\(\left(\frac{1}{83}\right)^{13}< \left(\frac{1}{81}\right)^{13}=\left(\frac{1}{3^4}\right)^{13}=\frac{1}{3^{52}}< \frac{1}{3^{45}}=\left(\frac{1}{243}\right)^9\Rightarrow\left(\frac{1}{83}\right)^{13}< \left(\frac{1}{243}\right)^9\)

b) 1990¹⁰ + 1990⁹

= 1990⁹ ( 1990 + 1 )

= 1990⁹ . 1991 < 1991¹⁰ = 1991⁹ . 1991

Vậy 1990¹⁰ + 1990⁹ < 1991¹⁰

Sửa đề: \(\left(\dfrac{1}{81}\right)^{13}\)

Ta có: \(\left(\dfrac{1}{243}\right)^9=\left(\dfrac{1}{3}\right)^{45}\)

\(\left(\dfrac{1}{81}\right)^{13}=\left(\dfrac{1}{3}\right)^{52}\)

mà \(\left(\dfrac{1}{3}\right)^{45}< \left(\dfrac{1}{3}\right)^{52}\)

nên \(\left(\dfrac{1}{243}\right)^9< \left(\dfrac{1}{81}\right)^{13}\)