Question

8*100^n/2^(2n+1)*5^(2n-2) Упростите выражение

Answer 1

$displaystyle frac{8cdot 100^n}{2^{2n+1}cdot 5^{2n-2}} = frac{2^3cdot (2^2cdot5^2)^n}{2^{2n+1}cdot 5^{2n-2}} = frac{2^3cdot 2^{2n}cdot 5^{2n}}{2^{2n+1}cdot 5^{2n-2}} = frac{2^{3+2n}cdot 5^{2n}}{2^{2n+1}cdot 5^{2n-2}} \\=2^2cdot 5^2=100$