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Lời giải:
a) Sai
Sửa lại: $(0,2)^{10}: (0,2)^5=(0,2)^{10-5}=(0,2)^5$
b) Sai
Sửa lại: $\frac{50^3}{125}=\frac{50^3}{5^3}=(\frac{50}{5})^3=10^3=1000$
c) Sai
Sửa lại: $\frac{8^{10}}{4^8}=\frac{(2^3)^{10}}{(2^2)^8}=\frac{2^{30}}{2^{16}}=2^{30-16}=2^{14}$
Lời giải:
a) Sai
Sửa lại: $(0,2)^{10}: (0,2)^5=(0,2)^{10-5}=(0,2)^5$
b) Sai
Sửa lại: $\frac{50^3}{125}=\frac{50^3}{5^3}=(\frac{50}{5})^3=10^3=1000$
c) Sai
Sửa lại: $\frac{8^{10}}{4^8}=\frac{(2^3)^{10}}{(2^2)^8}=\frac{2^{30}}{2^{16}}=2^{30-16}=2^{14}$

Các câu đúng: b,e
Các câu sai: a, c, d; f.
a) \(\left(-5\right)^2.\left(-5\right)^3=\left(-5\right)^5\);
c) \(\left(0,2\right)^{10}:\left(0,2\right)^5=\left(0,2\right)^{10-5}=0,2^5\);
d) \(\left[\left(-\dfrac{1}{7}\right)^2\right]^4=\left(-\dfrac{1}{7}\right)^{2.4}=\left(-\dfrac{1}{7}\right)^8\)
f \(\dfrac{8^{10}}{4^8}=\dfrac{\left(2^3\right)^5}{\left(2^2\right)^8}=\dfrac{2^{15}}{2^{16}}=\dfrac{1}{2}\)

\(a\)) \(\left(4^2.4^3\right):2^{10}\)
\(=4^5:2^{10}\)
\(=\left(2^2\right)^5:2^{10}\)
\(=2^{10}:2^{10}\)
\(=1\)
\(b\)) \(\left(0,6\right)^5:\left(0,2\right)^6\)
\(=\left(\frac{3}{5}\right)^5:\left(\frac{1}{5}\right)^6\)
\(=\frac{3^5}{5^5}:\frac{1^6}{5^6}\)
\(=\frac{3^5}{5^5}.5^6\)
\(=\frac{3^5.5^6}{5^5}\)
\(=3^5.5\)
\(=243.5\)
\(=1215\)
\(c\)) \(\left(2^7.9^3\right):\left(6^5.8^2\right)\)
\(=\left[2^7.\left(3^2\right)^3\right]:\left[\left(2.3\right)^5.\left(2^4\right)^2\right]\)
\(=\left(2^7.3^6\right):\left[2^5.3^5.2^8\right]\)
\(=\left(2^7.3^6\right).\left(\frac{1}{2^5.3^5.2^8}\right)\)
\(=\frac{2^7.3^6.1}{\left(2^5.2^8\right).3^5}\)
\(=\frac{2^7.3^6}{2^{13}.3^5}\)
\(=\frac{3}{2^6}\)
\(=\frac{3}{64}\)

tick nha:
a) (0,2)\(^8\) : (0,2)\(^{^{ }5}\) = (0,2)\(^3\)
b) \(\frac{6^{10}}{3^{10}}\) = 2\(^{10}\)
c) (0,5\(^2\))\(^3\) =(0,5)\(^6\)

\(a,8\cdot\frac23:4\cdot\frac13-10=\frac{16}{3}:\frac43-10\)
\(=\frac{16}{3}\cdot\frac34-10=4-10=-6\)
\(b,\frac25+\frac35:\left(-\frac{9}{10}\right)-\frac13\)
\(=\frac25+\frac35\cdot\left(-\frac{10}{9}\right)-\frac13\)
\(=\frac25+\left(-\frac23\right)-\frac13=\frac25-\left(\frac23+\frac13\right)\)
\(=\frac25-1=\frac25-\frac55=-\frac35\)
\(c,-1,25\cdot\left(-4,1\right)\cdot8+0,2\)
\(=\left(-1,25\cdot8\right)\cdot\left(-4,1\right)+0,2\)
\(=\left(-10\right)\cdot\left(-4,1\right)+0,2\)
\(=41+0,2=41,2\)
a; 8\(\frac23\) : 4\(\frac13\) - 10
= \(\frac{26}{3}\) : \(\frac{13}{3}\) - 10
= \(\frac{26}{3}\times\frac{3}{13}\) - 10
= 2 - 10
= - 8
b; \(\frac25+\frac35\) : (- \(\frac{9}{10}\)) - \(\frac13\)
= \(\frac25\) + \(\frac35\) x (- \(\frac{10}{9}\)) - \(\frac13\)
= \(\frac25\) - \(\frac23\) - \(\frac13\)
= \(\frac25\) - (\(\frac23+\frac13\))
= \(\frac25\) - 1
= \(\frac25\) - \(\frac55\)
= - \(\frac35\)
c; -1,25 x (-4,1) x 8 + 0,2
= (1,25 x 8) x 4,1 + 0,2
= 10 x 4,1 + 0,2
= 41 + 0,2
= 41,2
a) \(\frac{8^{10}}{4^8}=\frac{\left(2^3\right)^{10}}{\left(2^2\right)^8}=\frac{2^{30}}{2^{16}}=2^{14}=16384.\)
b) \(\frac{\left(0,2\right)^{10}}{\left(0,2\right)^5}=\left(0,2\right)^5=\frac{1}{3125}.\)
c) \(\frac{50^3}{125}=\frac{50^3}{5^3}=10^3=1000.\)
Chúc bạn học tốt!