Question

Scrieti sub forma unei singure puteri: a) 1,6×1,6^2×1,6^3×......×1,6^100;b) 2,25^5×2,25^10×2,25^15×....×2,25^50.

Answer 1

$\mathtt{a)1,6\cdot1,6^2\cdot1,6^3\cdot...\cdot1,6^{100}=1,6^{1+2+3+...+100}+1,6^{\frac{100(100+1)}{2}}=1,6^{5050}}$

$\mathtt{b)2,25^5\cdot 2,25^{10}\cdot 2,25^{15}\cdot...\cdot 2,25^{50}=2,25^{5+10+15+...+50}=} \\ \\ \mathtt{=2,25^{5(1+2+3+...+10)}=2,25^{5\cdot\frac{10(10+1)}{2}}=2,25^{55\cdot5}=2,25^{275}}$