If x = `y^(a), y = z^(b) and z = x^(c),` compute abc.

Answer

To solve the problem, we start with the given equations:

1. \( x = y^a \)
2. \( y = z^b \)
3. \( z = x^c \)

We need to find the product \( abc \).

### Step 1: Substitute \( y \) and \( z \) in terms of \( x \)

From the second equation, we can express \( y \) in terms of \( z \):
\[ y = z^b \]
Now, substitute the expression for \( z \) from the third equation:
\[ y = (x^c)^b = x^{bc} \]

### Step 2: Substitute \( y \) into the first equation

Now that we have \( y \) in terms of \( x \), we can substitute this into the first equation:
\[ x = (x^{bc})^a \]
This simplifies to:
\[ x = x^{abc} \]

### Step 3: Set the exponents equal

Since the bases are the same (assuming \( x \neq 0 \) and \( x \neq 1 \)), we can set the exponents equal to each other:
\[ 1 = abc \]

### Conclusion

Thus, we find that:
\[ abc = 1 \]