Dưới đây là các biểu thức số được viết dưới dạng lũy thừa của một số hữu tỉ:

**Bài 4:**

a. \( 2^9 \cdot 8^6 \)

Ta có: \( 8 = 2^3 \)

=> \( 8^6 = (2^3)^6 = 2^{18} \)

=> \( 2^9 \cdot 8^6 = 2^9 \cdot 2^{18} = 2^{27} \)

b. \( 36^6 : 6^{10} \)

Ta có: \( 36 = 6^2 \)

=> \( 36^6 = (6^2)^6 = 6^{12} \)

=> \( 36^6 : 6^{10} = 6^{12} : 6^{10} = 6^{2} = 36 \)

c. \( \frac{2^9 \cdot 9^{10}}{3^{11}} \)

Ta có: \( 9 = 3^2 \)

=> \( 9^{10} = (3^2)^{10} = 3^{20} \)

=> \( \frac{2^9 \cdot 9^{10}}{3^{11}} = \frac{2^9 \cdot 3^{20}}{3^{11}} = 2^9 \cdot 3^{9} = (2 \cdot 3)^9 = 6^9 \)

d. \( (0,25)^4 \cdot 16^8 \cdot 56 \cdot 8^7 \)

Ta có: \( 0,25 = \frac{1}{4} = 4^{-1} \)

=> \( (0,25)^4 = (4^{-1})^4 = 4^{-4} \)

Ta có: \( 16 = 4^2 \)

=> \( 16^8 = (4^2)^8 = 4^{16} \)

Ta có: \( 8 = 2^3 \)

=> \( 8^7 = (2^3)^7 = 2^{21} \)

=> \( (0,25)^4 \cdot 16^8 \cdot 56 \cdot 8^7 = 4^{-4} \cdot 4^{16} \cdot 56 \cdot 2^{21} = 4^{12} \cdot 56 \cdot 2^{21} \)

**Bài 5:**

a) \( A = 3^{19} \cdot \left( \frac{1}{9} \right)^9 \)

Ta có: \( \frac{1}{9} = 9^{-1} = (3^2)^{-1} = 3^{-2} \)

=> \( \left( \frac{1}{9} \right)^9 = (3^{-2})^9 = 3^{-18} \)

=> \( A = 3^{19} \cdot 3^{-18} = 3^{1} = 3 \)

b) \( B = \left( \frac{1}{16} \right)^{15} \cdot \left( \frac{1}{4} \right)^{28} \)

Ta có: \( \frac{1}{16} = 16^{-1} = (4^2)^{-1} = 4^{-2} \)

=> \( \left( \frac{1}{16} \right)^{15} = (4^{-2})^{15} = 4^{-30} \)

Ta có: \( \frac{1}{4} = 4^{-1} \)

=> \( \left( \frac{1}{4} \right)^{28} = (4^{-1})^{28} = 4^{-28} \)

=> \( B = 4^{-30} \cdot 4^{-28} = 4^{-58} \)

c) \( C = \frac{2^5 \cdot 5^{-10^6}}{3^5 \cdot 5^5} \)

=> \( C = \frac{2^5 \cdot 5^{-10^6}}{3^5 \cdot 5^5} = \frac{2^5}{3^5 \cdot 5^{10^6 + 5}} = \frac{2^5}{3^5 \cdot 5^{10^6 + 5}} \)

d) \( D = \frac{(0,25)^4 \cdot 2^9 + 6}{2^5 - 16} \)

Ta có: \( 0,25 = \frac{1}{4} = 4^{-1} \)

=> \( (0,25)^4 = (4^{-1})^4 = 4^{-4} \)

=> \( D = \frac{4^{-4} \cdot 2^9 + 6}{2^5 - 16} = \frac{4^{-4} \cdot 2^9 + 6}{2^5 - 2^4} = \frac{4^{-4} \cdot 2^9 + 6}{2^4(2 - 1)} = \frac{4^{-4} \cdot 2^9 + 6}{2^4} \)

=> \( D = \frac{4^{-4} \cdot 2^9 + 6}{2^4} = \frac{4^{-4} \cdot 2^9}{2^4} + \frac{6}{2^4} = 4^{-4} \cdot 2^{9-4} + \frac{6}{2^4} = 4^{-4} \cdot 2^5 + \frac{6}{2^4} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{6}{2^4} = 4^{-4} \cdot 2^5 + \frac{6}{16} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cdot 2^5 + \frac{3}{8} = 4^{-4} \cdot 2^5 + \frac{3}{8} \)

=> \( D = 4^{-4} \cd