## Solving the Equation: (n-27)^(3/2) = 64

This equation involves a fractional exponent, which can be a bit tricky at first. Let's break it down step-by-step to find the solution for 'n'.

### 1. Isolate the Term with the Exponent

The first step is to isolate the term with the fractional exponent: (n-27)^(3/2). We can do this by raising both sides of the equation to the power of (2/3).

**(n-27)^(3/2 * 2/3) = 64^(2/3)**

This simplifies to:

**(n-27) = 64^(2/3)**

### 2. Simplify the Right Side

Now, we need to simplify the right side of the equation. Remember that a fractional exponent means taking a root and then raising it to a power. In this case, 64^(2/3) means taking the cube root of 64 and then squaring the result:

**64^(2/3) = (³√64)² = 4² = 16**

### 3. Solve for 'n'

Now we have:

**(n-27) = 16**

To solve for 'n', simply add 27 to both sides of the equation:

**n = 16 + 27**

**n = 43**

### Conclusion

Therefore, the solution to the equation (n-27)^(3/2) = 64 is **n = 43**.