Question

19 la puterea 9 x 2 la puterea 3=
27 la puterea 7 : 3 la puterea 7=
100 la puterea 100 : 4 la puterea 100=
Dau coroana

Answer 1

Explicație pas cu pas:

${19}^{9} \times {2}^{3} = (19 \times 2)^{3} \times {19}^{6} = {38}^{3} \times 19^{6} = (38 \times 19)^{3} \times {19}^{3}$

${27}^{7} = {3}^{3 \times 7} = {3}^{21}$

${3}^{21 - 7} = {3}^{14}$

${100}^{100} \div {4}^{100} = (100 \div 4)^{100} = {25}^{100} = {5}^{200}$

Answer 2

19^9 · 2^3 = 19^(3·3) · 2^3 = (19^3)^3 · 2^3 = (19^3 · 2^3)^3

27^7 : 3^7 = (3^3)^7 : 3^7 = 3^(3·7) : 3^7 = 3^21 : 3^7 = 3^(21-7) = 3^14

100^100 : 4^100 = (4·25)^100 : 4^100 = 4^100 · 25^100 : 4^100 = 25^100 · (4^100 : 4^100) = 25^100 · 1 = 25^100