Step-by-step explanation:
[tex]5 \times {4}^{3n + 1} - 20 \times {8}^{2n} \\ \\ = 5 \times 4 \times {4}^{3n} - 20 \times {8}^{2n} \\ \\ = 20 \times ({4^{3} })^{n} - 20 \times {(8 ^{2} )}^{n} \\ \\ = 20 \times ({64})^{n} - 20 \times {(64)}^{n} \\ \\ = 20 \{{64}^{n} - {64}^{n} \} \\ \\ = 20 \times 0 \\ \\ = 0 \\ \\ \red{ \boxed{\therefore \: 5 \times {4}^{3n + 1} - 20 \times {8}^{2n} = 0}}[/tex]
