Is Option A or Option B the correct simplified expression of (x^4)^3.(x^−4) using the properties of integer exponents? Option A: x^8 Option B: x^3 Enter 1 for Option A or 2 for Option B.

Answer 1

To simplify the expression \((x^4)^3 \cdot (x^{-4})\), we can use the properties of exponents.

1. First, simplify \((x^4)^3\) using the property \( (a^m)^n = a^{mn} \): \[ (x^4)^3 = x^{4 \cdot 3} = x^{12} \]

2. Now, we multiply this result by \(x^{-4}\): \[ x^{12} \cdot x^{-4} \] Using the property \(a^m \cdot a^n = a^{m+n}\), we can combine the exponents: \[ x^{12 + (-4)} = x^{12 - 4} = x^8 \]

Thus, the simplified expression is \(x^8\).

Therefore, the correct answer is Option A: x^8 (1 for Option A).

The final answer is 1.