a) 8⁷ : 2⁷ = ( 8 : 2 )⁷ = 4⁷ = ( 2² )⁷ = 2¹⁴

b) 13¹⁰ . 2¹⁰ = ( 13 . 2 )¹⁰ = 26¹⁰

c) 17¹² . 25⁶ = 17¹² . ( 5² )⁶ = 17¹² . 5¹² = ( 17 . 5 )¹² = 85¹²

Bài 2:

a) \(\frac{2}{3}x+\frac{5}{7}+\frac{3}{10}\)

\(\Rightarrow\frac{2}{3}x=\frac{3}{10}-\frac{5}{7}\)

\(\Rightarrow\frac{2}{3}x=\frac{-29}{70}\)

\(\Rightarrow x=\frac{-29}{70}:\frac{2}{3}\)

\(\Rightarrow x=\frac{-87}{140}\)

b) \(\frac{3}{7}-x=\frac{1}{4}-\left(\frac{-3}{5}\right)\)

\(\Rightarrow\frac{3}{7}-x=\frac{1}{4}+\frac{3}{5}\)

\(\Rightarrow\frac{3}{7}-x=\frac{17}{20}\)

\(\Rightarrow x=\frac{3}{7}-\frac{17}{20}\)

\(\Rightarrow x=\frac{-59}{140}\)

c) \(\frac{-21}{13}x+1=\frac{-2}{3}\)

\(\Rightarrow\frac{-21}{13}x=\frac{-2}{3}-\frac{1}{3}\)

\(\Rightarrow\frac{-21}{13}x=-1\)

\(\Rightarrow x=\left(-1\right).\frac{-21}{13}\)

\(\Rightarrow x=\frac{13}{21}\)

Bài 4:

a) \(\left|x-1,5\right|=2\)

\(\Rightarrow\orbr{\begin{cases}x-1,5=2\\x-1,5=-2\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=2+1,5\\x=\left(-2\right)+1,5\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=3,5\\x=\frac{-1}{2}\end{cases}}\)

b) \(\left|x+\frac{3}{4}\right|-\frac{1}{2}=0\)

\(\Rightarrow\left|x+\frac{3}{4}\right|=\frac{1}{2}\)

\(\Rightarrow\orbr{\begin{cases}x+\frac{3}{4}=\frac{1}{2}\\x+\frac{3}{4}=\frac{-1}{2}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{1}{2}-\frac{3}{4}\\x=\frac{-1}{2}-\frac{3}{4}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{-1}{4}\\x=\frac{-5}{4}\end{cases}}\)

c) \(\left|x+\frac{4}{15}\right|-\left|-3.75\right|=-\left|-2,15\right|\)

\(\Rightarrow\left|x+\frac{4}{15}\right|-3,75=2,15\)

\(\Rightarrow\left|x+\frac{4}{15}\right|=5,9\)

\(\Rightarrow\orbr{\begin{cases}x+\frac{4}{15}=5,9\\x+\frac{4}{15}=-5,9\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=5,9-\frac{4}{15}\\x=-5,9-\frac{4}{15}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{169}{30}\\x=\frac{-37}{6}\end{cases}}\)