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