Question 183
a) Show that the value of the expression $\sqrt{9} \cdot \sqrt[3]{64} - \sqrt[3]{27} \cdot \sqrt{4}$ is a natural number.
b) Show that for every natural number $x$ the number $64^{-1} \cdot 8^{2x+4} - 24 \cdot 64^{x} + 4 \cdot 32^{x} \cdot 2^{x+3}$ is divisible by the number $\sqrt{9} \cdot \sqrt[3]{64} - \sqrt[3]{27} \cdot \sqrt{4}$.
b) Show that for every natural number $x$ the number $64^{-1} \cdot 8^{2x+4} - 24 \cdot 64^{x} + 4 \cdot 32^{x} \cdot 2^{x+3}$ is divisible by the number $\sqrt{9} \cdot \sqrt[3]{64} - \sqrt[3]{27} \cdot \sqrt{4}$.