Bài 4: Rút gọn phân số

\(=\dfrac{2^{19}\cdot3^9+2^{18}\cdot3^9\cdot5}{2^{19}\cdot3^9+2^{10}}\)

\(=\dfrac{2^{18}\cdot3^9\cdot\left(2+5\right)}{2^{10}\cdot\left(2^9\cdot3^9+1\right)}=\dfrac{2^8\cdot7\cdot3^9}{6^9+1}\)

\(\dfrac{3001500}{1010012}=\dfrac{3001500:116}{1010012:116}=\dfrac{25875}{8707}\)

\(\dfrac{\text{88.10.23+45+56+55}}{2}\) =\(\dfrac{20240+45+56+55}{2}\) =\(\dfrac{20396}{2}\) =10198

20240+45+56+55220240+45+56+552 =

=10198

\(\dfrac{9^{14}\cdot25^5\cdot8^7}{18^2\cdot625^3\cdot24^3}\)

\(=\dfrac{3^{42}\cdot5^{10}\cdot2^{21}}{2^2\cdot3^4\cdot5^{12}\cdot2^9\cdot3^3}=\dfrac{3^{42}\cdot5^{10}\cdot2^{21}}{2^{11}\cdot3^7\cdot5^{12}}\)

\(=\dfrac{3^{35}}{5^2}\cdot2^{10}\)

Lời giải:
Xét hiệu:

$(5^{200}+3)(5^{202}+1)-(5^{201}+3)(5^{201}+1)$

$=5^{402}+5^{200}+3.5^{202}+3-(5^{402}+4.5^{201}+3)$

$=5^{200}+3.5^{202}-4.5^{201}$

$=5^{200}(1-5)+3.5^{201}(5-1)$

$=-4.5^{200}+4.3.5^{201}=4.5^{200}(15-1)=14.4.5^{200}>0$

$\Rightarrow (5^{200}+3)(5^{202}+1)> (5^{201}+3)(5^{201}+1)$

$\Rightarrow M> N$

a: -21/39 rút gọn bằng-7/13

b;-7/13; -42/78

tối giản

 1289/1296 phân số đã tối giãng

Tối giản rồi

ủa mik giúp r mà

−68 / 76 = -19/ 17

Dạng tổng quát:

−68 / 76 = ( − 19 / 17 ). k / k với ( K∈Z )

\(\dfrac{13\cdot3^n}{6^m}\)

\(=\dfrac{13\cdot3^n}{3^m\cdot2^m}\)

\(=\dfrac{13}{2^m}\cdot3^{n-m}\)

1: -9/80=-36/320

17/320=17/320

2: -7/10=-231/300

1/-33=-1/33=-10/330

3: -5/14=-50/140

3/20=21/140

9/-70=-9/70=-18/140

4: -10/-42=10/42=5/21=220/924

-3/28=-99/924

-55/132=-385/924