) \( 2^{\frac{x}{3}}=\frac{1}{128} \) Solve for \( x \)

To solve the equation \( 2^{\frac{x}{3}}=\frac{1}{128} \), we start by recognizing that \( 128 \) can be expressed as a power of \( 2 \): \( 128 = 2^7 \). Therefore, we can rewrite \( \frac{1}{128} \) as \( 2^{-7} \). This transforms the equation into: \[ 2^{\frac{x}{3}} = 2^{-7} \] Since the bases are the same, we can set the exponents equal to each other: \[ \frac{x}{3} = -7 \] Now, solve for \( x \) by multiplying both sides by \( 3 \): \[ x = -21 \] Thus, the solution is \( x = -21 \).