Question

Utilizando as propriedades de potências, simplifique as expressões:
a)$\frac{25}{5^{3} }$
b)$2^{4}.3^{4}.6$
c)$(7^{6} )^{2} . 49^{5} . 7^{2^{2}$
d)$\frac{9^{2} . 11^{4}}{16}$

Answer 1

$a)\ \frac{25}{5^3} =\frac{5^2}{5^3} =5^{2-3}=5^{-1}\\\\b) \ 2^4\cdot3^4\cdot6=2^4\cdot3^4\cdot2\cdot3=2^{4+1}\cdot3^{4+1}=2^{5}\cdot3^{5}=(2\cdot3)^{5}=6^5\\\\c)\ \big(7^6\big)^2\cdot49^5\cdot7^{2^2}=7^{6\cdot2}\cdot(7^2)^5\cdot7^{4}=7^{12}\cdot7^{2\cdot5}\cdot7^{4}=7^{12}\cdot7^{10}\cdot7^{4}=7^{12+10+4}=7^{26}\\\\d)\ \frac{9^2\cdot11^4}{16}=\frac{(3^2)^2\cdot11^4}{2^4}=\frac{3^{2\cdot2}\cdot11^4}{2^4}=\frac{3^{4}\cdot11^4}{2^4}=\frac{(3\cdot11)^4}{2^4}=\frac{33^4}{2^4}=\big(\frac{33}{2} \big)^4$