Question

Função Exponencial básico.

a) ( \frac{ 1 }{2})^{-2} + ( \frac{ 1 }{3})^{-1}

b) [( -\frac{ 5 }{3})^{-1} + ( \frac{ 5 }{2})^{-1}]^{-1}ex]

c) [ 3^{-1} - (-3)^{-1}]^{-1}

d) 6. ( \frac{2}{3})^{2} + 4. (- \frac{3}{2})^{-2}

Answer 1

a)
$( \frac{ 1 }{2})^{-2} + ( \frac{ 1 }{3})^{-1}=\\ \\2^2+3=4+3=7$

b)
$[( -\frac{ 5 }{3})^{-1} + ( \frac{ 5 }{2})^{-1}]^{-1}=\\ \\ (-\frac{3}{5} +\frac{2}{5})^{-1}=(-\frac{1}{5})^{-1}=-5$

c)
$[ 3^{-1} - (-3)^{-1}]^{-1} =\\ \\ (\frac{1}{3}-(-\frac{1}{3}))^{-1}=\\ \\ (\frac{1} {3}+\frac{1}{3})^{-1}=\\ \\ (\frac{2}{3})^{-1}=\frac{3}{2}$

d)
$6. ( \frac{2}{3})^{2} + 4. (- \frac{3}{2})^{-2} =\\ \\ 6.\frac{4}{9}+4(-\frac{4}{9})=\\ \\ \frac{24}{9}-\frac{16}{9}=\frac{8}{9}$