If `x ne 0 and (x^(4))(x^(-4))=y,` what is y?

Answer

To solve the equation \( (x^4)(x^{-4}) = y \), we will use the laws of exponents. Here is the step-by-step solution:

### Step 1: Identify the expression
We start with the expression:
\[ y = (x^4)(x^{-4}) \]

### Step 2: Apply the laws of exponents
According to the laws of exponents, when we multiply two powers with the same base, we add the exponents:
\[ x^m \cdot x^n = x^{m+n} \]
In our case, we have:
\[ y = x^{4 + (-4)} \]

### Step 3: Simplify the exponent
Now, we simplify the exponent:
\[ y = x^{4 - 4} = x^0 \]

### Step 4: Use the property of exponents
We know that any non-zero base raised to the power of zero is equal to 1:
\[ x^0 = 1 \quad \text{(since \( x \neq 0 \))} \]

### Step 5: Conclude the value of y
Thus, we conclude that:
\[ y = 1 \]

### Final Answer:
The value of \( y \) is \( 1 \).

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