Question

1) Determine o valor da expressão:
a)  ( 3^6  . 3^-2  ) : 3^4 =
b) (2^2 . 2^-3 . 3^-1 . 3^2 )^2 =
c) (10^-2 . 10^-3 . 10^-4 ) ÷ (10^-1 . 10^-6 ) =

Answer 1

a)

$( {3}^{6} \times {3}^{ - 2} ) \div {3}^{4} = {3}^{4} \div {3}^{4} = {3}^{0} = 1$

b)

$( {2}^{2} \times {2}^{ - 3} \times {3}^{ - 1} \times {3}^{2} ) ^{2} = ( {2}^{ - 1} \times {3}^{1} ) {}^{2} = (\frac{1}{2} \times 3) {}^{2} = ( \frac{3}{2} ) {}^{2} = \frac{9}{4}$

c)

$( {10}^{ - 2} \times {10}^{ - 3} \times {10}^{ - 4} ) \div ( {10}^{1} \times {10}^{ - 6} ) = {10}^{ - 9} \div {10}^{ - 7} = {10}^{ - 2} = ( \frac{1}{10} ) {}^{2} = \frac{1}{100}$