Question

calcule as potências a seguir:

(-0,4666...) elevado a -2

(0,0181818...) elevado a -1

Answer 1

=Retificando a resposta=

$1)(-0,4666...)^-2\\x=0,466\\ \left \{ {{10x=46,666 \atop {100x=46,666}} \right. \\100x-10x=46,666-4,666\\90x=42\\x= \frac{42^{\div6}}{90^{\div6}} =\ \textgreater \ \boxed{x= \frac{7}{15}}\\\\( -\frac{7}{15})^-2= (-\frac{15}{7})^2=\ \textgreater \ \boxed{\boxed{\frac{225}{49}}}\\\\\\ 2)(0,01818...)^-1\\x=0,01818\\ \left \{ {{10x=0,1818} \atop {1000x=18,1818}} \right.\\1000x-10x=18,1818-0,1818\\990x=18\\x=\frac{18^{\div6}}{990^{\div6}}=\ \textgreater \ \boxed{x=\frac{1}{55}} \\\\\\ (\frac{1}{55})^-1=(\frac{55}{1})^1=\ \textgreater \ \boxed{\boxed{55}}$