Question

QUESTÃO 3.
Considere a expressão numérica seguinte:
3
3
5
5
-C
6
A potência de expoente negativo equivalente a essa expressão é:
a)-(5/6)12 b) (-5/6) c) (6/5)-1/2 d) (5/6)-1/2​

Answer 1

$\ \ \ \sqrt{\Big({\frac{5}{3} }\Big)^3\cdot\Big({\frac{1}{2} }\Big)^3} \div\frac{5}{6} \\\\=\sqrt{\Big({\frac{5}{3} \cdot \frac{1}{2} }\Big)^3} \div\frac{5}{6}\\\\ =\sqrt{\Big({\frac{5}{6} }\Big)^3} \div\frac{5}{6} \\\\=\Big({\frac{5}{6} }\Big)^\frac{3}{2} \div\Big(\frac{5}{6} \Big)^1\\\\=\Big({\frac{5}{6} }\Big)^{\frac{3}{2}-1}$

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