After you multiply both sides by $L$, what can you divide both sides by to isolate $r^4$ on one side of the equation?

Once you have an equation of the form $r^4 = \text{(expression)}$, what operation do you use to solve for $r$? Think about what undoes raising to the fourth power.

Express the fourth root using an exponent of $1/4$, then look for the choice that has the same structure and the correct placement of $Q$, $k$, and $L$ in the fraction.

In Desmos, enter simple positive values for the parameters, for example: Q = 10, k = 2, and L = 5. These will let you numerically test each answer choice.

For each option, type a separate expression for $r$ using the chosen values of $Q$, $k$, and $L$, for example: rA = sqrt(Q*L/k), rB = (Q*L/k)^(1/4), rC = k*Q^4/L, and rD = (k/(Q*L))^(1/4).

For each $r$ you defined, compute the flow rate given by the original formula, for example: QA = k*rA^4/L, QB = k*rB^4/L, and so on. Compare each result to your original value of Q. The expression for $r$ whose computed flow rate matches the original Q is the correct choice.

You are given

The goal is to rewrite this equation so that $r$ is alone on one side and the expression on the other side uses only $Q$, $k$, and $L$.

First, eliminate the denominator $L$ by multiplying both sides of the equation by $L$:

Now divide both sides by $k$ to isolate $r^4$:

So you have an expression for $r^4$ in terms of $Q$, $k$, and $L$.

To solve for $r$ from $r^4$, you need to apply the inverse operation of raising to the fourth power, which is taking the fourth root. In general, if $x^4 = a$, then $x$ is the fourth root of $a$, or $x = a^{1/4}$.

Apply this idea to the equation you found for $r^4$.

From

take the fourth root of both sides:

This matches choice B, so the correct expression for the radius is $r = \left(\dfrac{Q L}{k}\right)^{1/4}$.