Question

URGENTE, es para dentro de 1 hora, es Mates


1) Expresa como producto de potencias la base de la cual sea un numero primo (estan en la foto)

Answer 1

a)

$(6^{3}8^{2})^{3}=((2*3)^{3}(2^{3})^{2})^{3}=(2^{3}3^{3}2^{6})^{3}=(2^{3})^{3}(3^{3})^{3}(2^{6})^{3}=2^{9}3^{9}2^{18}=2^{27}3^{9}$

b)

$(12^{3}18^{4})^{5}=(12^{3})^{5}(18^{4})^{5}=12^{15}18^{20}=(2^{2}*3)^{15}(2*3^{2})^{20}=(2^{2})^{15}3^{15}2^{20}(3^{2})^{20}=2^{30}3^{15}2^{20}3^{40}=2^{50}3^{55}$

c)

$[(-4)^{6}6^{2}]^{4}=((-4)^{6})^{4}(6^{2})^{4}=(-4)^{24}6^{8}=(-1)^{24}(2^{2})^{24}(2*3)^{8}=2^{48}2^{8}3^{8}=2^{56}3^{8}$

d)

$[3^{5}(-6)^{4}]^{2}=(3^{5})^{2}((-6)^{4})^{2}=3^{10}(-6)^{8}=3^{10}(-1)^{8}(2*3)^{8}=3^{10}2^{8}3^{8}=2^{8}3^{18}$

espero te ayude