Solve the Equation by Expressing Each Side as a Power $$32 ^ { x } = \frac { 1 } { \sqrt { 2 } }$$

Multiple Choice

Solve the equation by expressing each side as a power of the same base and then equating exponents.
- $$32 ^ { x } = \frac { 1 } { \sqrt { 2 } }$$

A) $\left\{ - \frac { 1 } { 10 } \right\}$
B) $\left\{ \frac { 1 } { 10 } \right\}$
C) $\left\{ - \frac { 1 } { 5 } \right\}$
D) $\{ - 5 \}$