Is Option A or Option B the correct simplified expression of (x4)3.(x−4)

Question

using the properties of integer exponents?

Option A: x8

Option B: x3


Enter 1 for Option A or 2 for Option B.(1 point)

Answer 1

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

First, we simplify \( (x^4)^3 \): \[ (x^4)^3 = x^{4 \cdot 3} = x^{12} \]

Now we have: \[ x^{12} \cdot x^{-4} \]

Using the property that \( a^m \cdot a^n = a^{m+n} \), we combine the exponents: \[ x^{12} \cdot x^{-4} = x^{12 + (-4)} = x^{12 - 4} = x^{8} \]

So, the correct simplified expression is \( x^{8} \).

Therefore, the correct answer is Option A.

Enter 1 for Option A.