a) Ta có: \(\dfrac{8\cdot9-4\cdot15}{12\cdot7-180}\)

\(=\dfrac{4\cdot18-4\cdot15}{12\cdot7-12\cdot15}\)

\(=\dfrac{4\cdot\left(18-15\right)}{12\cdot\left(7-15\right)}\)

\(=\dfrac{4\cdot3}{12\cdot\left(-8\right)}\)

\(=\dfrac{12}{12\cdot\left(-8\right)}=\dfrac{-1}{8}\)

b) Ta có: \(\dfrac{2^3\cdot3}{2^2\cdot3^2\cdot5}\)

\(=\dfrac{2^2\cdot2\cdot3}{2^2\cdot3\cdot3\cdot5}\)

\(=\dfrac{2}{3\cdot5}=\dfrac{2}{15}\)

=2

a) \(\dfrac{2727-101}{3.303+404}=\dfrac{2626}{909+404}=\dfrac{2626}{1313}=2\)

b) \(\dfrac{8.9-4.15}{12.7-180}=\dfrac{72-60}{84-180}=\dfrac{12}{-96}=\dfrac{-1}{8}\)

c) \(\dfrac{-19}{3^2.7.11}=\dfrac{-19}{9.7.11}=\dfrac{-19}{63.11}=\dfrac{-19}{693}\)

d) \(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{2^{12}.3^{10}+120.6^9}{2^{12}.3^{12}-6^{11}}=\dfrac{2^2.6^{10}+20.6.6^9}{6^{12}-6^{11}}=\dfrac{4.6^{10}+20.6^{10}}{6^{11}\left(6-1\right)}=\dfrac{\left(4+20\right).6^{10}}{5.6^{11}}=\dfrac{24}{30}=\dfrac{4}{5}\)

a) \(\dfrac{-3}{5}.51\dfrac{11}{13}+\dfrac{3}{5}.21\dfrac{11}{13}\)

\(=\dfrac{-3}{5}.\left(51\dfrac{11}{13}-21\dfrac{11}{13}\right)\)

\(=\dfrac{-3}{5}.30\)

\(=-18.\)

b) \(\left|\dfrac{-3}{4}\right|.\left|-\dfrac{2}{3}\right|=\dfrac{3}{4}.\dfrac{2}{3}=\dfrac{1}{2}\).

c) \(\dfrac{-3}{5}+5\dfrac{1}{13}-\dfrac{2}{3}+1\dfrac{3}{5}-\dfrac{11}{33}\)

\(=\left(1\dfrac{3}{5}-\dfrac{3}{5}\right)+5\dfrac{1}{13}-\left(\dfrac{2}{3}+\dfrac{11}{33}\right)\)

\(=1+\dfrac{66}{13}-1\)

\(=\dfrac{66}{13}.\)

d) \(\dfrac{3}{4}.\sqrt{16}-10.\sqrt{0,81}\)

\(=\dfrac{3}{4}.4-10.\dfrac{9}{10}\)

\(=3.9\)

\(=27.\)

e) \(\left(\dfrac{3}{4}\right)^3:\left(\dfrac{-3}{8}\right)^3=\dfrac{3^3}{4^3}.\dfrac{\left(-8\right)^3}{3^3}=\left(\dfrac{-8}{4}\right)^3=\left(-2\right)^3=-8\)

f) \(\dfrac{6^4.15^3}{8.9^3.10^3}=\dfrac{2^4.3^4.3^3.5^3}{2^3.3^6.2^3.5^3}=\dfrac{2.3^7}{2^3.3^6}=\dfrac{3}{2^2}=\dfrac{3}{4}.\)

a,\(\left(-1,25\right).14,7.\left(-8\right)\)

\(=\left[\left(-1,25\right).\left(-8\right)\right].14,7\)

\(=10.14,7=147\)

b, \(\dfrac{3}{4}-1\dfrac{1}{6}\)

\(=\dfrac{3}{4}-\dfrac{7}{6}\)

\(=\dfrac{9-14}{12}=\dfrac{-5}{12}\)

câu c: Mình không biết bạn có gõ sai không, bạn coi đề lại xem.

d, \(\left|\dfrac{-3}{4}\right|.\left|-\dfrac{2}{3}\right|\)

\(=\dfrac{3}{4}.\dfrac{2}{3}=\dfrac{1.1}{2.1}=\dfrac{1}{2}\)

e, ?

c: \(=\dfrac{-3}{5}\left(51+\dfrac{11}{13}-21-\dfrac{11}{13}\right)=\dfrac{-3}{5}\cdot30=-18\)

e: \(=\dfrac{-3}{5}+1+\dfrac{3}{5}+5+\dfrac{1}{13}-\dfrac{2}{3}-\dfrac{1}{3}\)

\(=\dfrac{1}{13}\)

h: \(=\dfrac{2^4\cdot3^4\cdot3^3\cdot5^3}{2^3\cdot3^6\cdot2^3\cdot5^3}=\dfrac{3}{2}\)

f: \(=\dfrac{3}{4}\cdot4-10\cdot\dfrac{9}{10}=3-9=-6\)

\(\dfrac{8^4.15^4}{12^3.10^3}=\dfrac{2^{12}.3^4.5^4}{2^6.3^3.2^3.5^3}=2^3.3.5=120\)

Vì \(-\left|2x+3\right|\le0\Rightarrow4-\left|2x+3\right|\le4\)

\(\Rightarrow A\le4\forall x\)

Dấu "=" xảy ra khi \(\left|2x+3\right|=0\Rightarrow2x+3=0\)

\(\Rightarrow x=\dfrac{-3}{2}\)

Vậy \(MAX_A=A\) khi x = -3/2.

( -1,25) . 14,7. ( -8 )

= \(\frac{-5}{4}\). \(\frac{147}{10}\)\(.\frac{\left(-8\right)}{1}\)

= \(\frac{\left(-5\right).147.\left(-8\right)}{4.10.1}.\)

= \(\frac{\left[\left(-5\right).\left(-8\right)\right].147}{\left(4.10\right).1}\)

= \(\left[\frac{-5}{4}.\frac{-8}{10}\right].147\)

=147

\(\frac{3}{4}-1\frac{1}{6}=\frac{3}{4}-\frac{7}{6}\)

\(=\frac{9-14}{12}\)

\(=\frac{-5}{12}\)

Ta có: \(\frac{2^5.7+2^5}{2^5.5^2-2^5.3}\) = \(\frac{2^5.\left(7+1\right)}{2^5.\left(5^2-3\right)}\) = \(\frac{2^5.8}{2^5.22}\) = \(\frac{8}{22}\) =\(\frac{56}{154}\)

​\(\frac{3^4.5-3^6}{3^4.13+3^4}\) = \(\frac{3^4.\left(5-3^2\right)}{3^4.\left(13+1\right)}\) = \(\frac{3^4.\left(-4\right)}{3^4.14}\) = \(\frac{-4}{14}\)= \(\frac{-44}{154}\)

`@` `\text {Ans}`

`\downarrow`

\(\dfrac{2^8-2^3}{2^5-1}=\dfrac{2^3\left(2^5-1\right)}{2^5-1}=\dfrac{2^3}{1}=2^3=8\)

_____

\(\dfrac{4^8\cdot9^4}{6^6\cdot8^3}\)

`=`\(\dfrac{\left(2^2\right)^8\cdot\left(3^2\right)^4}{2^6\cdot3^6\cdot\left(2^3\right)^3}\)

`=`\(\dfrac{2^{16}\cdot3^8}{2^6\cdot3^6\cdot2^9}\)

`=`\(\dfrac{2^{16}\cdot3^8}{2^{15}\cdot3^6}\)

`=`\(\dfrac{3^2}{2}\) `=`\(\dfrac{9}{2}\)

______

\(\dfrac{27^4\cdot2^3-3^{10}\cdot4^3}{6^4\cdot9^3}\)

`=`\(\dfrac{\left(3^3\right)^4\cdot2^3-3^{10}\cdot\left(2^2\right)^3}{2^4\cdot3^4\cdot\left(3^2\right)^3}\)

`=`\(\dfrac{3^{12}\cdot2^3-3^{10}\cdot2^6}{2^4\cdot3^4\cdot3^6}\)

`=`\(\dfrac{3^{10}\cdot\left(3^2\cdot2^3-2^6\right)}{3^{10}\cdot2^4}\)

`=`\(\dfrac{72-2^6}{2^4}=\dfrac{8}{16}=\dfrac{1}{2}\)

\(\dfrac{2^8-2^3}{2^5-1}=\dfrac{2^3\left(2^5-1\right)}{2^5-1}=2^3=8\)

\(\dfrac{4^8.9^4}{6^6.8^3}=\dfrac{2^{16}.3^8}{2^6.3^6.2^9}=2.3^2=18\)

\(\dfrac{27^4.2^3-3^{10}.4^3}{6^4.9^3}=\dfrac{3^{12}.2^3-3^{10}.2^6}{2^4.3^4.3^6}=\dfrac{2^3.3^{10}.\left(3^2-2^3\right)}{2^4.3^{10}}=\dfrac{9-8}{2}=\dfrac{1}{2}\)

Sơ đồ thể hiện tác động tiêu cực của việc gia tăng dân số quá nhanh ở đới nóng đối với tài nguyên, môi trường.