To find the product of the two given expressions [tex]\(\left(7 x^2 y^3\right)\left(3 x^5 y^8\right)\)[/tex], follow these steps:
1. Multiply the coefficients:
- The coefficients are 7 and 3.
- When we multiply these coefficients together, we get [tex]\(7 \times 3 = 21\)[/tex].
2. Combine the powers of [tex]\(x\)[/tex]:
- In the first term [tex]\(7 x^2 y^3\)[/tex], the power of [tex]\(x\)[/tex] is 2.
- In the second term [tex]\(3 x^5 y^8\)[/tex], the power of [tex]\(x\)[/tex] is 5.
- When you multiply terms with the same base, you add their exponents: [tex]\(x^2 \times x^5 = x^{2+5} = x^7\)[/tex].
3. Combine the powers of [tex]\(y\)[/tex]:
- In the first term [tex]\(7 x^2 y^3\)[/tex], the power of [tex]\(y\)[/tex] is 3.
- In the second term [tex]\(3 x^5 y^8\)[/tex], the power of [tex]\(y\)[/tex] is 8.
- Similarly, when you multiply terms with the same base, you add their exponents: [tex]\(y^3 \times y^8 = y^{3+8} = y^{11}\)[/tex].
Putting it all together, the product of [tex]\(\left(7 x^2 y^3\right)\left(3 x^5 y^8\right)\)[/tex] is:
[tex]\[
21 x^7 y^{11}
\][/tex]
Therefore, the correct answer is:
[tex]\[
21 x^7 y^{11}
\][/tex]
