The problem in your image asks to find the inverse of the function:

$f(x) = \left(\frac{x}{8}\right)^{\frac{1}{7}}$

To find the inverse function $f^{-1}(x)$, we follow these steps:

Step 1: Set $y = f(x)$

$y = \left(\frac{x}{8}\right)^{\frac{1}{7}}$

Step 2: Solve for $x$ in terms of $y$

We need to solve for $x$ from the equation $y = \left(\frac{x}{8}\right)^{\frac{1}{7}}$.

First, raise both sides of the equation to the power of 7 to eliminate the exponent on the right-hand side: $y^7 = \frac{x}{8}$

Step 3: Multiply both sides by 8 to isolate $x$:

$x = 8y^7$

Step 4: Replace $y$ with $x$ to write the inverse function:

$f^{-1}(x) = 8x^7$

So, the inverse function is:

[ f^{-1}(x)