How to find r in the equation s = (6y⁹ / a⁵ r)?

To isolate the variable r in the equation s = (6y⁹ / a⁵ r), it is essential to rearrange the equation using algebraic manipulation.

Starting with the given equation:

s = (6y⁹ / a⁵ r),

you can multiply both sides of the equation by a⁵ r to eliminate the fraction, yielding:

s * a⁵ r = 6y⁹.

Next, to solve for r, divide both sides by s and a⁵:

r = (6y⁹) / (s * a⁵).

This indicates that r is calculated as the ratio of 6y⁹ to the product of s and a⁵. Hence, the correct form to express r is 6y⁹ / (sa⁵).

In this context, the other options either mix terms in ways that don't maintain the integrity of the original equation or fail to express r correctly. The key takeaway is to recognize how to manipulate equations algebraically to isolate a variable, leading to the correct expression for r.