Answer :
To simplify the expression [tex]\((-4 x^7) \cdot (8 x^2)\)[/tex], follow these steps:
1. Multiply the coefficients:
- We have the coefficients [tex]\(-4\)[/tex] and [tex]\(8\)[/tex]. Multiply these together: [tex]\(-4 \times 8 = -32\)[/tex].
2. Apply the exponent property for like bases:
- The base [tex]\(x\)[/tex] appears in both terms: [tex]\(x^7\)[/tex] and [tex]\(x^2\)[/tex].
- When you multiply terms with the same base, you add their exponents:
[tex]\[
x^{7} \times x^{2} = x^{7+2} = x^{9}
\][/tex]
3. Combine the results:
- Combine the multiplied coefficient with the combined exponents:
[tex]\[
-32 \times x^9 = -32x^9
\][/tex]
Therefore, the simplified form of the expression [tex]\((-4 x^7) \cdot (8 x^2)\)[/tex] is [tex]\(-32x^9\)[/tex].
This means the correct answer is [tex]\(-32 x^9\)[/tex].
1. Multiply the coefficients:
- We have the coefficients [tex]\(-4\)[/tex] and [tex]\(8\)[/tex]. Multiply these together: [tex]\(-4 \times 8 = -32\)[/tex].
2. Apply the exponent property for like bases:
- The base [tex]\(x\)[/tex] appears in both terms: [tex]\(x^7\)[/tex] and [tex]\(x^2\)[/tex].
- When you multiply terms with the same base, you add their exponents:
[tex]\[
x^{7} \times x^{2} = x^{7+2} = x^{9}
\][/tex]
3. Combine the results:
- Combine the multiplied coefficient with the combined exponents:
[tex]\[
-32 \times x^9 = -32x^9
\][/tex]
Therefore, the simplified form of the expression [tex]\((-4 x^7) \cdot (8 x^2)\)[/tex] is [tex]\(-32x^9\)[/tex].
This means the correct answer is [tex]\(-32 x^9\)[/tex].
