Question

Упростить 4^n+3-4^n+1 все деленное на 15

Answer 1

$\frac{4^{n+3}-4^{n+1}}{15}=\frac{4^n\cdot4^3-4^n\cdot4}{15}=\frac{64\cdot4^n-4\cdot4^n}{15}=\frac{60\cdot4^n}{15}=\frac{60\cdot4^n}{15}=4\cdot4^n=\\\\4^{n+1}=(2^2)^{n+1}=2^{2(n+1)}$