Please follow these step-by-step instructions to solve the equation (t + 6)^(4/5) = 2:
1. To begin, we will look at the equation (t + 6)^(4/5) = 2. Our goal is to solve for t.
2. The first step in solving this equation is to rid of the 4/5 power of (t + 6).
3. To do this, take both sides of the equation to the 5/4 power, as the 5/4 power is an inverse operation of the 4/5 power.
4. This gives us (t + 6) = 2^(5/4). Now, we have the exponent used has been reverted to the original state, or in other words, removed.
5. The next step is to isolate t. We can do this by subtracting 6 from both sides of the equation.
6. Subtracting 6 from both sides, the equation becomes t = 2^(5/4) - 6.
7. Now, let's simplify. We can calculate the value of 2^(5/4), and subtract 6 from that value.
8. After performing the calculation, we obtain t = -3.621585769994558.
So, the solution to the equation (t + 6)^(4/5) = 2 is t = -3.621585769994558.