OlympiadHardAlgebra7–9

The number $2^{2026} + 2^{2023}$ can be written as $9 \times 2^{k}$ . What is $k$ ?

O número $2^{2026} + 2^{2023}$ pode escrever-se como $9 \times 2^{k}$ . Quanto vale $k$ ?

Answer options

Solution

Take out the smaller power: $2^{2026} + 2^{2023} = 2^{2023}(2^{3} + 1) = 2^{2023} \times 9$ , so $k = 2023$ .