Answer :
To simplify the expression [tex]\((4x^3)^3\)[/tex], follow these steps:
1. Understand the Expression: The expression [tex]\((4x^3)^3\)[/tex] means you are taking the entire term [tex]\(4x^3\)[/tex] to the power of 3.
2. Apply the Power of a Product Rule: The power of a product rule states that [tex]\((ab)^n = a^n \cdot b^n\)[/tex]. In our expression, apply it as follows:
[tex]\[
(4x^3)^3 = (4)^3 \cdot (x^3)^3
\][/tex]
3. Calculate [tex]\(4^3\)[/tex]: Multiply 4 by itself three times:
[tex]\[
4^3 = 4 \times 4 \times 4 = 64
\][/tex]
4. Calculate [tex]\((x^3)^3\)[/tex]: Use the power of a power rule, which states that [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]:
[tex]\[
(x^3)^3 = x^{3 \cdot 3} = x^9
\][/tex]
5. Combine the Results: Put together the results from step 3 and step 4:
[tex]\[
64 \cdot x^9
\][/tex]
Thus, the simplified expression is [tex]\(64x^9\)[/tex].
The correct answer is (A) [tex]\(64x^9\)[/tex].
1. Understand the Expression: The expression [tex]\((4x^3)^3\)[/tex] means you are taking the entire term [tex]\(4x^3\)[/tex] to the power of 3.
2. Apply the Power of a Product Rule: The power of a product rule states that [tex]\((ab)^n = a^n \cdot b^n\)[/tex]. In our expression, apply it as follows:
[tex]\[
(4x^3)^3 = (4)^3 \cdot (x^3)^3
\][/tex]
3. Calculate [tex]\(4^3\)[/tex]: Multiply 4 by itself three times:
[tex]\[
4^3 = 4 \times 4 \times 4 = 64
\][/tex]
4. Calculate [tex]\((x^3)^3\)[/tex]: Use the power of a power rule, which states that [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]:
[tex]\[
(x^3)^3 = x^{3 \cdot 3} = x^9
\][/tex]
5. Combine the Results: Put together the results from step 3 and step 4:
[tex]\[
64 \cdot x^9
\][/tex]
Thus, the simplified expression is [tex]\(64x^9\)[/tex].
The correct answer is (A) [tex]\(64x^9\)[/tex].
