16^5-8^6

To simplify \( 16^5 - 8^6 \), we can rewrite the numbers using base 2:

1. \( 16 = 2^4 \) and \( 8 = 2^3 \).
2. Therefore, we can express \( 16^5 \) and \( 8^6 \) in terms of base 2:

\[ 16^5 = (2^4)^5 = 2^{20} \]

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

Now we can substitute these into the expression:

\[ 16^5 - 8^6 = 2^{20} - 2^{18} \]

Next, we can factor out the common term \( 2^{18} \):

\[ 2^{20} - 2^{18} = 2^{18}(2^2 - 1) = 2^{18}(4 - 1) = 2^{18} \cdot 3 \]

Thus, the final result is:

\[ 16^5 - 8^6 = 3 \cdot 2^{18} \]

If you need a numerical value:

\[ 2^{18} = 262144 \quad \text{(since \( 2^10 = 1024 \) and \( 2^8 = 256 \))} \]

Now calculate:

\[ 3 \cdot 2^{18} = 3 \cdot 262144 = 786432 \]

Therefore, the final answer is:

\[ 16^5 - 8^6 = 786432 \]