Question

Aplique todas as propriedades da potência


A)
$(3 {}^{4} ) ^{2} .3 ^{2} \div 3 {}^{4}$
B)
$(2 {}^{7}) ^{2} \div 2 ^{5} .2 ^{9}$
C)
$2 ^{7} . \: 2 ^{5} \div (2 ^{3}) ^{2}$

D)
$5 ^{9} \div 5 ^{3}.5 ^{2}$

Answer 1

A)
$(3^{4} )^{2}.3^{2} :3^{4}$
$=3^{8}.3^{2} :3^{4}$
$=3^{8+2} :3^{4}$
$=3^{10} :3^{4}$
$=3^{10-4}$
$=3^{6}$

B)
$( 2^{7} )^{2} : 2^{5} . 2^{9} = 2^{7*2}: 2^{5+9} = 2^{14}:2^{14} = 2^{14-14} =2^{0}=1$

C)
$2^{7} . 2^{5} :( 2^{3} )^{2} = 2^{7+5}: 2^{6} = 2^{12} : 2^{6} = 2^{12-6} = 2^{6}$


D)
$5^{9}: 5^{3}. 5^{2} = 5^{9}: 5^{3+2} = 5^{9}: 5^{5} = 5^{9-5} = 5^{4}$