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a, ( 1/2 - 13/14 ) : 5/7 - ( -2/21 + 1/7 ) : 5/7
= ( 7/14 - 13/14 ) : 5/7 - ( -2/21 + 3/21 ) : 5/7
= -3/7 : 5/7 - 1/21 : 5/7
= -3/7 . 7/5 - 1/21 . 7/5
= ( -3/7 - 1/21 ) . 7/5
= ( -9/7+ -1/21 ) . 7/5
= -10/21 . 7/5
= -2/3
b, (68/5 + 19/4 ) - 43/5
= 68/5 + 19/4 - 43/5
= ( 68/5 - 43/5 ) + 19/4
= 5 +19/4
= 39/4
c, ( 93/11 + 29/8 ) - 38/11
= 93/11 + 29/8 - 38/11
= ( 93/11 - 38/11 ) + 29/8
= 5 + 29/8
=69/8
d, 4/9 : ( -1/7 ) + 59/9 : ( -1/7 )
= 4/9 . -7 + 59/9 . -7
= ( 4/9 + 59/9 ) . -7
= 7 . -7
= -49

\(\frac{3}{5}.\frac{13}{46}-\frac{1}{10}.\frac{16}{23}=\frac{3.13}{5.46}-\frac{1.16}{10.23}\)
\(=\frac{39}{230}-\frac{8}{115}=\frac{39}{230}-\frac{8.2}{115.2}\)
\(=\frac{39}{230}-\frac{16}{230}=\frac{39-16}{230}\)
\(=\frac{23}{230}=\frac{1}{10}\)

A = \(\dfrac{1}{2}\) - 0,75 + \(\dfrac{5}{4}\) - \(\dfrac{6}{12}\)
A = 0,5 - 0,75 + 1,25 - 0,5
A = (0,5 - 0,5) + (1,25 - 0,75)
A = 0,5
B = (-\(\dfrac{1}{7}\))0 - 22.(\(\dfrac{2}{3}\))2
B = 1 - 22. \(\dfrac{4}{9}\)
B = 1 - \(\dfrac{88}{9}\)
B = - \(\dfrac{79}{9}\)
\(b,\left(-\dfrac{1}{5}\right)^{10}:\left(\dfrac{1}{5}\right)^7\)
Vì \(\left(-\dfrac{1}{5}\right)^{10}=\left(\dfrac{1}{5}\right)^{10}\)nên
\(\Rightarrow\left(\dfrac{1}{5}\right)^{10}:\left(\dfrac{1}{5}\right)^7\)
\(\Rightarrow\left(\dfrac{1}{5}\right)^{10-7}\)
\(\Rightarrow\left(\dfrac{1}{5}\right)^3=\dfrac{1}{125}\)
Công thức:
\(a^m\cdot a^n=a^{m+n}\)
\(a^m:a^n=a^{m-n}\)
`(-1/5)^10 : (1/5)^7`
`= (1/5)^10 : (1/5)^7`
`= (1/5)^(10-7)`
`= (1/5)^3`
`= 1/125`