Decide what values of the variable cannot possibly be solutions for the equation.
-$$8 x ^ { - 2 / 5 } + 14 x ^ { - 1 / 5 } + 6 = 0$$
A) $\left\{ - 1 , - \frac { 4 } { 3 } \right\}$
B) $\left\{ - 1 , - \frac { 1024 } { 243 } \right\}$
C) $\{ 2,3 \}$
D) $\left\{ 1 , \frac { 1024 } { 243 } \right\}$

Question

Quizplus · Accepted Answer

The equation involves negative exponents, which means the variable $x$ is in the denominator when the expression is rewritten. Therefore, any real number value for $x$ is valid as long as it does not make the denominator zero. However, since the exponents are fractional and negative, $x$ cannot be zero because it would make the expression undefined. The choices given are specific values, but none of them would inherently make the expression undefined based on the form of the equation given. The correct answer is based on understanding that $x = 0$ is the value that cannot be a solution, but since this option is not provided, the explanation focuses on why the specific values given in the choices do not directly relate to the equation's solvability.

Decide What Values of the Variable Cannot Possibly Be Solutions 8x−2/5+14x−1/5+6=08 x ^ { - 2 / 5 } + 14 x ^ { - 1 / 5 } + 6 = 08x−2/5+14x−1/5+6=0

Decide What Values of the Variable Cannot Possibly Be Solutions $8 x ^ { - 2 / 5 } + 14 x ^ { - 1 / 5 } + 6 = 0$