Question

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

Answer 1

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