Answer :
To multiply the expression [tex]\(5v \cdot 2v^8x^9 \cdot 4x^6\)[/tex], we can follow these steps:
1. Multiply the coefficients:
- Start by multiplying the numerical coefficients together:
[tex]\[
5 \times 2 \times 4 = 40
\][/tex]
2. Combine the [tex]\(v\)[/tex] terms:
- When multiplying variables with exponents, you add the exponents if the bases are the same.
- For [tex]\(v\)[/tex], we have [tex]\(v\)[/tex] and [tex]\(v^8\)[/tex], which means:
[tex]\[
v^1 \cdot v^8 = v^{1+8} = v^9
\][/tex]
3. Combine the [tex]\(x\)[/tex] terms:
- Similarly, for [tex]\(x\)[/tex] we have [tex]\(x^9\)[/tex] and [tex]\(x^6\)[/tex], so:
[tex]\[
x^9 \cdot x^6 = x^{9+6} = x^{15}
\][/tex]
4. Write the final expression:
- Combining all these parts, the product of the expression is:
[tex]\[
40v^9x^{15}
\][/tex]
So, the final result of multiplying [tex]\(5v \cdot 2v^8x^9 \cdot 4x^6\)[/tex] is [tex]\(40v^9x^{15}\)[/tex].
1. Multiply the coefficients:
- Start by multiplying the numerical coefficients together:
[tex]\[
5 \times 2 \times 4 = 40
\][/tex]
2. Combine the [tex]\(v\)[/tex] terms:
- When multiplying variables with exponents, you add the exponents if the bases are the same.
- For [tex]\(v\)[/tex], we have [tex]\(v\)[/tex] and [tex]\(v^8\)[/tex], which means:
[tex]\[
v^1 \cdot v^8 = v^{1+8} = v^9
\][/tex]
3. Combine the [tex]\(x\)[/tex] terms:
- Similarly, for [tex]\(x\)[/tex] we have [tex]\(x^9\)[/tex] and [tex]\(x^6\)[/tex], so:
[tex]\[
x^9 \cdot x^6 = x^{9+6} = x^{15}
\][/tex]
4. Write the final expression:
- Combining all these parts, the product of the expression is:
[tex]\[
40v^9x^{15}
\][/tex]
So, the final result of multiplying [tex]\(5v \cdot 2v^8x^9 \cdot 4x^6\)[/tex] is [tex]\(40v^9x^{15}\)[/tex].
