Answer :
Let's work through the solution step-by-step:
We need to expand the expression [tex]\((2x^2)^3\)[/tex] without exponents.
1. Expand the coefficient (constant number):
- Start with the coefficient, which is 2. We need to multiply 2 by itself three times because of the exponent 3.
- So, you calculate [tex]\(2^3 = 2 \times 2 \times 2 = 8\)[/tex].
2. Expand the variable part:
- Look at the variable part, which is [tex]\(x^2\)[/tex]. The exponent 3 outside the parentheses applies to this as well.
- According to the rules of exponents, [tex]\((x^m)^n = x^{m \times n}\)[/tex].
- So, [tex]\((x^2)^3 = x^{2 \times 3} = x^6\)[/tex].
Combining these steps, the expanded form of [tex]\((2x^2)^3\)[/tex] is [tex]\(8x^6\)[/tex].
Therefore, [tex]\((2x^2)^3\)[/tex] without exponents is [tex]\(8x^6\)[/tex].
We need to expand the expression [tex]\((2x^2)^3\)[/tex] without exponents.
1. Expand the coefficient (constant number):
- Start with the coefficient, which is 2. We need to multiply 2 by itself three times because of the exponent 3.
- So, you calculate [tex]\(2^3 = 2 \times 2 \times 2 = 8\)[/tex].
2. Expand the variable part:
- Look at the variable part, which is [tex]\(x^2\)[/tex]. The exponent 3 outside the parentheses applies to this as well.
- According to the rules of exponents, [tex]\((x^m)^n = x^{m \times n}\)[/tex].
- So, [tex]\((x^2)^3 = x^{2 \times 3} = x^6\)[/tex].
Combining these steps, the expanded form of [tex]\((2x^2)^3\)[/tex] is [tex]\(8x^6\)[/tex].
Therefore, [tex]\((2x^2)^3\)[/tex] without exponents is [tex]\(8x^6\)[/tex].
