Question

Is Option A or Option B the correct simplified expression of (4x3)3 using the properties of integer exponents? Option A: 4x9 Option B: 64x9 Enter 1 for Option A or 2 for Option B.

Answer 1

To simplify the expression \((4x^3)^3\) using the properties of integer exponents, we can apply the power of a product property which states that \((ab)^n = a^n b^n\).

1. Apply the power to the constant and the variable separately:

\[
(4x^3)^3 = 4^3 (x^3)^3
\]

2. Calculate \(4^3\):

\[
4^3 = 64
\]

3. Calculate \((x^3)^3\):

\[
(x^3)^3 = x^{3 \times 3} = x^9
\]

4. Combine the results:

\[
(4x^3)^3 = 64x^9
\]

Now, comparing with the given options:
- Option A: \(4x^9\)
- Option B: \(64x^9\)

The correct simplified expression is Option B: \(64x^9\).

So, the answer is **2** for Option B.