a) \(\left(\dfrac{3}{7}+\dfrac{1}{2}\right)^2=\left(\dfrac{6}{14}+\dfrac{7}{17}\right)^2=\left(\dfrac{13}{12}\right)^2=\dfrac{13^2}{12^2}=\dfrac{169}{144}\)

b)\(\left(\dfrac{3}{4}-\dfrac{5}{6}\right)^2=\left(\dfrac{9}{12}-\dfrac{10}{12}\right)^2=\left(\dfrac{-1}{12}\right)^2=\dfrac{\left(-1\right)^2}{12^2}=\dfrac{1}{144}\)

c)\(\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{5^4.5^4.2^8}{5^{10}.2^{10}}=\dfrac{5^8.2^8}{5^8.5^2.2^8.2^2}=\dfrac{1}{5^2.2^2}=\dfrac{1}{25.4}=\dfrac{1}{100}\)

d)\(\left(\dfrac{-10}{3}\right)^5.\left(\dfrac{-6}{5}\right)^4=\dfrac{\left(-10\right)^5.\left(-6\right)^4}{3^5.5^4}=\dfrac{\left(-2\right)^5.5^5.2^4.3^4}{3^4.3.5^4}=\dfrac{\left(-2\right)^5.5.5^42^4}{3.5^4}=\dfrac{\left(-2\right)^5.5.2^4}{3}=\dfrac{-2560}{3}=-853\dfrac{1}{3}\)

Mark the letter A, B, C, or D on your answer sheet to show the underlined part that needs correction in each of the following questions

Exceeding speed limits and fail to wear safety belts are two common causes of automobile death.

A. Exceeding        

B. fail 

C. safety belts        

D. causes

\(A=0,5-\left|x-3,5\right|\)

Ta có \(\left|x-3,5\right|\)\(\ge\)0 Với mọi x

\(\Rightarrow\) 0,5-\(\left|x-3,5\right|\)\(\le\)0,5 Với mọi x

\(\Rightarrow Amax\) =0,5 khi x-3,5=0

\(\Leftrightarrow\) Amax=0,5 khi x=3,5

B thì tương tự

C=1,7+\(\left|3,4-x\right|\)

Ta có \(\left|3,4-x\right|\)\(\ge\)0 Với mọi x

\(\Rightarrow\)1,7+\(\left|3,4-x\right|\)\(\ge\)1,7 Với mọi x

\(\Rightarrow\)Cmin=1,7 khi \(3,4-x=0\)

\(\Leftrightarrow\)Cmin=1,7 khi x=3,4

D=\(\left|x+2,8\right|\)\(-\) 3,5

Ta có \(\left|x+2,8\right|\ge0\)Với mọi x

\(\Rightarrow\left|x+2,8\right|-3,5\ge-3,5\) Với mọi x

\(\Rightarrow Cmin\)=-3,5 khi x+2,8=0

\(\Leftrightarrow\) Cmin=-3,5 khi x=-2,8