Answer :
Sure, let's simplify the expression step-by-step:
The given expression is [tex]\((-4x^7) \cdot (8x^2)\)[/tex].
1. Multiply the coefficients:
- The coefficients in the expression are [tex]\(-4\)[/tex] and [tex]\(8\)[/tex].
- Multiply these together: [tex]\(-4 \times 8 = -32\)[/tex].
2. Apply the exponent properties to the variable [tex]\(x\)[/tex]:
- The exponents for [tex]\(x\)[/tex] are [tex]\(7\)[/tex] and [tex]\(2\)[/tex].
- According to the exponent rule, when you multiply expressions with the same base, you add the exponents: [tex]\(x^7 \times x^2 = x^{7 + 2} = x^9\)[/tex].
Combining these results, the simplified expression is [tex]\(-32x^9\)[/tex].
So, the correct answer matching our work is [tex]\(-32x^9\)[/tex].
The given expression is [tex]\((-4x^7) \cdot (8x^2)\)[/tex].
1. Multiply the coefficients:
- The coefficients in the expression are [tex]\(-4\)[/tex] and [tex]\(8\)[/tex].
- Multiply these together: [tex]\(-4 \times 8 = -32\)[/tex].
2. Apply the exponent properties to the variable [tex]\(x\)[/tex]:
- The exponents for [tex]\(x\)[/tex] are [tex]\(7\)[/tex] and [tex]\(2\)[/tex].
- According to the exponent rule, when you multiply expressions with the same base, you add the exponents: [tex]\(x^7 \times x^2 = x^{7 + 2} = x^9\)[/tex].
Combining these results, the simplified expression is [tex]\(-32x^9\)[/tex].
So, the correct answer matching our work is [tex]\(-32x^9\)[/tex].
