Question

Realiza las siguientes operaciones aplicando las propie-
dades de la potenciación.​

Answer 1

Respuesta:

16) 1

17) $-\frac{1}{5}$

18) $\frac{2}{7^5}$

Explicación paso a paso:

16)

  $2+2^-^1-(\frac{1}{2})^-^1-(\frac{1}{2})^1+ 2^0\\\\2+\frac{1}{2}-2-\frac{1}{2} +1\\\\2-2+1+\frac{1}{2}- \frac{1}{2} \\\\2-2+1\\\\1$

17)

$\frac{(3^-^1+2^-^1)^-^1}{(3^-^1-2^-^1)^-^1} \\\\(\frac{3^-^1+2^-^1}{3^-^1-2^-^1})^-^1\\\\\frac{3^-^1-2^-^1}{3^-^1+2^-^1}\\\\\frac{\frac{1}{3}-\frac{1}{2}}{\frac{1}{3}+\frac{1}{2}}\\\\\frac{\frac{2-3}{6}}{\frac{2+3}{6}}\\\\\frac{\frac{-1}{6}}{\frac{5}{6}}\\\\\frac{-1}{5}$

18)

$[\frac{7^-^2+49^-^1}{343}]*[\frac{8^-^2+2^-^6}{2^-^5}]\\\\~[\frac{7^-^2+(7^2)^-^1}{343}]*[\frac{(2^3)^-^2+2^-^6}{2^-^5}]\\\\~[\frac{7^-^2+7^-^2}{343}]*[\frac{2^-^6+2^-^6}{2^-^5}]\\\\~[\frac{7^-^2}{343}+\frac{7^-^2}{343}]*[\frac{2^-^6}{2^-^5}+\frac{2^-^6}{2^-^5}]\\\\~[\frac{7^-^2}{7^3}+\frac{7^-^2}{7^3}]*[\frac{2^-^6}{2^-^5}+\frac{2^-^6}{2^-^5}]\\\\~[(7)^-^2^-^3+(7)^-^2^-^3]*[2^-^6^-^(^-^5^)}+2^-^6^-^(^-^5^)]\\\\~[(7)^-^5+(7)^-^5]*[2^-^6^+^5}+2^-^6^+^5]\\\\~[7^-^5+7^-^5]*[2^-^1}+2^-^1]$

$~[\frac{1}{7^5}+\frac{1}{7^5}]*[\frac{1}{2}+\frac{1}{2}]\\\\~[\frac{1+1}{7^5}]*[\frac{1+1}{2}]\\\\~[\frac{2}{7^5}]*[\frac{2}{2}]\\\\\frac{2}{7^5}*1\\\\\frac{2}{7^5} =\frac{2}{16807}$