Tính nhanh biết

To solve these exponential expressions, we need to apply the rules of exponents. Here are the solutions:

1. \( 7^7 \)
\[ 7^7 = 823543 \]

2. \( 5^5 \)
\[ 5^5 = 3125 \]

3. \( 4^4 \)
\[ 4^4 = 256 \]

4. \( 2^2 \)
\[ 2^2 = 4 \]

5. \( 3^3 \)
\[ 3^3 = 27 \]

6. \( (-5)^4 \)
\[ (-5)^4 = 625 \]

7. \( (-2) \cdot (-2)^6 \)
\[ (-2) \cdot (-2)^6 = (-2) \cdot 64 = -128 \]

8. \( (-6)^5 \cdot (-6) \)
\[ (-6)^5 \cdot (-6) = (-7776) \cdot (-6) = 46656 \]

9. \( (-0.1)^1 \cdot (-0.1)^1 \)
\[ (-0.1)^1 \cdot (-0.1)^1 = (-0.1) \cdot (-0.1) = 0.01 \]

10. \( (-0.2)^1 \cdot (-0.2)^3 \)
\[ (-0.2)^1 \cdot (-0.2)^3 = (-0.2) \cdot (-0.008) = 0.0016 \]

11. \( \left( \frac{4}{5} \right)^1 \cdot \left( \frac{4}{5} \right)^1 \)
\[ \left( \frac{4}{5} \right)^1 \cdot \left( \frac{4}{5} \right)^1 = \left( \frac{4}{5} \right)^2 = \frac{16}{25} \]

12. \( \left( \frac{1}{2} \right)^1 \cdot \left( \frac{1}{2} \right)^2 \)
\[ \left( \frac{1}{2} \right)^1 \cdot \left( \frac{1}{2} \right)^2 = \left( \frac{1}{2} \right)^3 = \frac{1}{8} \]

13. \( A = 3^{19} \left( \frac{1}{9} \right) \)
\[ A = 3^{19} \cdot 9^{-1} = 3^{19} \cdot 3^{-2} = 3^{17} \]

14. \( 8 \left( \frac{2}{3} \right)^3 \)
\[ 8 \left( \frac{2}{3} \right)^3 = 8 \cdot \frac{8}{27} = \frac{64}{27} \]

15. \( 12^2 \left( \frac{1}{12} \right)^{10} \)
\[ 12^2 \left( \frac{1}{12} \right)^{10} = 12^2 \cdot 12^{-10} = 12^{-8} = \frac{1}{12^8} = \frac{1}{429981696} \]