Chào bạn! Mình sẽ giúp bạn giải các bài toán này nhé.

1. \(\frac{4^{5 \cdot 10} \cdot 5^{10}}{7^{5 \cdot 10}}\)
\[
= \frac{(4 \cdot 5)^{10}}{7^{50}}
= \frac{20^{10}}{7^{50}}
\]

2. \(\frac{(0,8)^5}{(0,4)^6}\)
\[
= \frac{(0,8)^5}{(0,4)^6}
= \frac{(2 \cdot 0,4)^5}{(0,4)^6}
= \frac{2^5 \cdot (0,4)^5}{(0,4)^6}
= \frac{2^5}{0,4}
= \frac{32}{0,4}
= 80
\]

3. \(\frac{2^{15} \cdot 9^4}{6^3 \cdot 8^3}\)
\[
= \frac{2^{15} \cdot (3^2)^4}{(2 \cdot 3)^3 \cdot (2^3)^3}
= \frac{2^{15} \cdot 3^8}{2^3 \cdot 3^3 \cdot 2^9}
= \frac{2^{15} \cdot 3^8}{2^{12} \cdot 3^3}
= 2^{15-12} \cdot 3^{8-3}
= 2^3 \cdot 3^5
= 8 \cdot 243
= 1944
\]

4. \(\frac{8^{10} + 4^{10}}{8^4 + 4^{11}}\)
\[
= \frac{(2^3)^{10} + (2^2)^{10}}{(2^3)^4 + (2^2)^{11}}
= \frac{2^{30} + 2^{20}}{2^{12} + 2^{22}}
= \frac{2^{20}(2^{10} + 1)}{2^{12}(1 + 2^{10})}
= \frac{2^{20} \cdot (2^{10} + 1)}{2^{12} \cdot (2^{10} + 1)}
= \frac{2^{20}}{2^{12}}
= 2^{20-12}
= 2^8
= 256
\]

5. \((0,25)^3 \cdot 32\)
\[
= (0,25)^3 \cdot 32
= \left(\frac{1}{4}\right)^3 \cdot 32
= \frac{1}{64} \cdot 32
= \frac{32}{64}
= \frac{1}{2}
= 0,5
\]

6. \(\frac{8^2 \cdot 4^5}{2^{20}}\)
\[
= \frac{(2^3)^2 \cdot (2^2)^5}{2^{20}}
= \frac{2^6 \cdot 2^{10}}{2^{20}}
= \frac{2^{16}}{2^{20}}
= 2^{16-20}
= 2^{-4}
= \frac{1}{2^4}
= \frac{1}{16}
\]

7. \((-0,125)^3 \cdot 80^4\)
\[
= (-0,125)^3 \cdot 80^4
= \left(-\frac{1}{8}\right)^3 \cdot (8 \cdot 10)^4
= -\frac{1}{512} \cdot 8^4 \cdot 10^4
= -\frac{1}{512} \cdot 4096 \cdot 10000
= -\frac{40960000}{512}
= -80000
\]

8. \(\frac{8^{11} \cdot 3^{17}}{27^{10} \cdot 9^{15}}\)
\[
= \frac{(2^3)^{11} \cdot 3^{17}}{(3^3)^{10} \cdot (3^2)^{15}}
= \frac{2^{33} \cdot 3^{17}}{3^{30} \cdot 3^{30}}
= \frac{2^{33} \cdot 3^{17}}{3^{60}}
= 2^{33} \cdot 3^{17-60}
= 2^{33} \cdot 3^{-43}
= \frac{2^{33}}{3^{43}}
\]

Hy vọng những lời giải trên sẽ giúp bạn hiểu rõ hơn về cách giải các bài toán này!