Question

Resolva as expressões com potências
a) $3^{2} - 3^{-2} / 3^{2} + 3^{-2}$
b) $2^{-1} - (-2) ^{2} +(-2) ^{-1} / 2^{2} + 2^{-2}$

Answer 1

a)
$(3^2-3^{-2})\div(3^2+3^{-2})= \\ \\ (9- \frac{1}{9} )\div(9+ \frac{1}{9} )= \\ \\ ( \frac{81-1}{9} )\div( \frac{81+1}{9} )= \\ \\ \frac{80}{9} \div \frac{82}{9} = \\ \\ \frac{80}{\not9} \times \frac{\not9}{82} = \frac{80}{82} = \frac{40}{41}$

b)
$(2^{-1}-(-2)^2+(-2)^{-1})\div(2^2+2^{-2})= \\ \\ ( \frac{1}{2} -(+4)+(- \frac{1}{2} )\div(4+ \frac{1}{4} )= \\ \\ (\not \frac{1}{2} -4-\not \frac{1}{2} )\div( \frac{17}{4} )= \\ \\ (-4)\times( \frac{4}{17} )=- \frac{16}{17}$

Answer 2

a)

3² - 3⁻²/3² + 3⁻²
9 - 1/3²/3² + 1/3²
9 - 1/9 / 9 + 1/9
81/9 - 1/9 / 81/9 + 1/9
80/9 / 82/9
80/9 * 9/82 
80/82
= 40/41

b)

2⁻¹ - (-2)² + (-2)⁻¹/2² + 2⁻²
1/2 - 4 - 1/2 / 4 + 1/4
-4/ 17/4
-4 * 4/17
-16/17