## Solving the Equation (7+x)^(3/2) = 64

This equation presents a challenge due to the fractional exponent. Let's break down the steps to find the solution for *x*.

### 1. Isolate the Exponent Term

To isolate the term with the fractional exponent, we need to get rid of the 64. We achieve this by raising both sides of the equation to the power of 2/3. This is the reciprocal of the exponent on the left side:

```
[(7+x)^(3/2)]^(2/3) = 64^(2/3)
```

This simplifies to:

```
7 + x = 64^(2/3)
```

### 2. Calculate the Right Side

We can rewrite 64 as 4^3. This makes the calculation easier:

```
7 + x = (4^3)^(2/3)
```

Using the rule (a^m)^n = a^(m*n):

```
7 + x = 4^(3 * 2/3)
```

```
7 + x = 4^2
```

```
7 + x = 16
```

### 3. Solve for x

Now we have a simple linear equation. Subtract 7 from both sides:

```
x = 16 - 7
```

```
x = 9
```

### Conclusion

Therefore, the solution to the equation (7+x)^(3/2) = 64 is **x = 9**.