Question

\(\dfrac{16^3\cdot3^{10}+144\cdot6^9}{4^6\cdot3^{12}+6^{11}}\)

rút gọn p/s trên

giúp MEOWW ❤

Answer 1

\(\dfrac{16^3.3^{10}+144.6^9}{4^6.3^{12}+6^{11}}\)

=\(\dfrac{16^3.3^{10}+144.6^9}{4.4.4.4.4.4.3^{12}+6^{11}}\)

=\(\dfrac{16^3.3^{10}+144.6^9}{16.16.16.3^{12}+6^{11}}\)

=\(\dfrac{16^3.3^{10}+4.6^2.6^9}{16^3.3^{12}+6^{11}}\)

=\(\dfrac{4.6^{11}}{3^2+6^{11}}\)

=\(\dfrac{4}{9}\)

Ko chắc

Answer 2

tử số  4⁶.3¹⁰+144.6⁹ = 2¹².3¹⁰+2.2³.3.3.6⁹

= 6⁹.(2³.3)+(2³.3).6⁹.6 = 6⁹.(2³.3).(6+1) = 6⁹.(2³.3).7 = 6⁹.2.3.2².7

= 6¹⁰.4.7

mẫu số 4⁶.3¹²+6¹¹ = 2¹².3¹²+6¹¹ = 6¹²+6¹¹ = 6¹¹.6+6¹¹ 

= 6¹¹.(6+1) = 6¹¹.7

\(\dfrac{16^{3}.3^{10}+144.6^{9}}{4^{6}.3^{12}.6^{11}}=\dfrac{6^{10}.4.7}{6^{11}.7}\)=\(\dfrac{4}{6}=\dfrac{2}{3}\)

 mà cậu trình bày trên phân số nhé để nhanh thì mình chia ra thôi

Answer 3

\(\dfrac{16^3.3^{10}+144.6^9}{4^6.3^{12}+6^{11}}\) 

=\(\dfrac{2^{12}.3^{10}+2.2^3.3.3.6^9}{2^{12}.3^{12}+6^{11}}\) 

=\(\dfrac{6^9.\left(2^3.3\right)+\left(2^3.3\right).6^9.6}{6^{12}+6^{11}}\) 

=\(\dfrac{6^9.\left(2^3.3\right).\left(6+1\right)}{6^{11}.6+6^{11}}\) 

=\(\dfrac{6^9.2.3.2^2.7}{6^{11}.\left(6+1\right)}\) 

=\(\dfrac{6^{10}.4.7}{6^{11}.7}\) 

=\(\dfrac{4}{6}=\dfrac{2}{3}\)