4^5•8^8

To simplify \( 4^5 \cdot 8^8 \), we can express both numbers in terms of base 2:

1. \( 4^5 \) can be rewritten as \( (2^2)^5 = 2^{10} \).
2. \( 8^8 \) can be rewritten as \( (2^3)^8 = 2^{24} \).

Now, we can combine the two results:

\[ 4^5 \cdot 8^8 = 2^{10} \cdot 2^{24} \]

Using the property of exponents that states \( a^m \cdot a^n = a^{m+n} \):

\[ 2^{10} \cdot 2^{24} = 2^{10 + 24} = 2^{34} \]

Thus, the expression \( 4^5 \cdot 8^8 \) simplifies to \( 2^{34} \).