Answer :
To simplify the expression [tex]\((4x^2)^3\)[/tex], we'll break it down into simple steps:
1. Apply the Power Rule: When you have an expression of the form [tex]\((a^m)^n\)[/tex], it simplifies to [tex]\(a^{m \cdot n}\)[/tex]. This means we will apply this rule separately for both the numerical part and the variable part of the expression [tex]\((4x^2)^3\)[/tex].
2. Simplify the Numerical Part:
- First, look at the number 4. We need to raise 4 to the power of 3.
- That means [tex]\(4^3\)[/tex].
- Calculating [tex]\(4^3\)[/tex], we get:
[tex]\[
4 \times 4 \times 4 = 64
\][/tex]
3. Simplify the Variable Part:
- Next, consider the variable part [tex]\(x^2\)[/tex]. We need to raise this to the power of 3 as well.
- This means [tex]\((x^2)^3\)[/tex].
- According to the power rule, multiply the exponents: [tex]\(2 \times 3 = 6\)[/tex].
- So, [tex]\((x^2)^3 = x^6\)[/tex].
4. Combine Both Parts:
- Combine the results from both steps above to get the expression:
[tex]\[
64x^6
\][/tex]
Therefore, the expression [tex]\((4x^2)^3\)[/tex] is equivalent to [tex]\(64x^6\)[/tex]. The correct choice from the given options is:
- [tex]\(64 x^6\)[/tex]
1. Apply the Power Rule: When you have an expression of the form [tex]\((a^m)^n\)[/tex], it simplifies to [tex]\(a^{m \cdot n}\)[/tex]. This means we will apply this rule separately for both the numerical part and the variable part of the expression [tex]\((4x^2)^3\)[/tex].
2. Simplify the Numerical Part:
- First, look at the number 4. We need to raise 4 to the power of 3.
- That means [tex]\(4^3\)[/tex].
- Calculating [tex]\(4^3\)[/tex], we get:
[tex]\[
4 \times 4 \times 4 = 64
\][/tex]
3. Simplify the Variable Part:
- Next, consider the variable part [tex]\(x^2\)[/tex]. We need to raise this to the power of 3 as well.
- This means [tex]\((x^2)^3\)[/tex].
- According to the power rule, multiply the exponents: [tex]\(2 \times 3 = 6\)[/tex].
- So, [tex]\((x^2)^3 = x^6\)[/tex].
4. Combine Both Parts:
- Combine the results from both steps above to get the expression:
[tex]\[
64x^6
\][/tex]
Therefore, the expression [tex]\((4x^2)^3\)[/tex] is equivalent to [tex]\(64x^6\)[/tex]. The correct choice from the given options is:
- [tex]\(64 x^6\)[/tex]
