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Answer :
Let's go through the given expression step by step:
We start with the expression: [tex]\( 8(2x^2)^3 \)[/tex].
1. Expand inside the parentheses:
- Inside the parentheses, we have [tex]\( (2x^2)^3 \)[/tex].
- To expand this, we apply the power of a power rule: [tex]\((a^m)^n = a^{m \times n}\)[/tex].
- Therefore, [tex]\((2x^2)^3 = (2)^3 \times (x^2)^3\)[/tex].
2. Simplify the powers:
- [tex]\( (2)^3 = 8\)[/tex].
- [tex]\( (x^2)^3 = x^{2 \times 3} = x^6 \)[/tex].
3. Combine these results:
- So, [tex]\( (2x^2)^3 = 8 \times x^6\)[/tex].
4. Multiply by the coefficient outside the parentheses:
- We have [tex]\( 8(2x^2)^3 \)[/tex], which becomes [tex]\( 8 \times (8 \times x^6) \)[/tex].
5. Finish the multiplication:
- Multiply the numbers: [tex]\( 8 \times 8 = 64\)[/tex].
Thus, the entire expression simplifies to: [tex]\( 64x^6 \)[/tex].
This is the simplified form of the original expression.
We start with the expression: [tex]\( 8(2x^2)^3 \)[/tex].
1. Expand inside the parentheses:
- Inside the parentheses, we have [tex]\( (2x^2)^3 \)[/tex].
- To expand this, we apply the power of a power rule: [tex]\((a^m)^n = a^{m \times n}\)[/tex].
- Therefore, [tex]\((2x^2)^3 = (2)^3 \times (x^2)^3\)[/tex].
2. Simplify the powers:
- [tex]\( (2)^3 = 8\)[/tex].
- [tex]\( (x^2)^3 = x^{2 \times 3} = x^6 \)[/tex].
3. Combine these results:
- So, [tex]\( (2x^2)^3 = 8 \times x^6\)[/tex].
4. Multiply by the coefficient outside the parentheses:
- We have [tex]\( 8(2x^2)^3 \)[/tex], which becomes [tex]\( 8 \times (8 \times x^6) \)[/tex].
5. Finish the multiplication:
- Multiply the numbers: [tex]\( 8 \times 8 = 64\)[/tex].
Thus, the entire expression simplifies to: [tex]\( 64x^6 \)[/tex].
This is the simplified form of the original expression.
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