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.