To find the product of the given expression [tex]\(\left(7 x^2 y^3\right)\left(3 x^5 y^8\right)\)[/tex], follow these steps:
1. Multiply the constants: The constants given are 7 and 3. Multiplying these together, we have:
[tex]\[
7 \times 3 = 21
\][/tex]
2. Combine the exponents of [tex]\(x\)[/tex]: The expression contains [tex]\(x^2\)[/tex] and [tex]\(x^5\)[/tex]. When multiplying terms with the same base, their exponents are added together:
[tex]\[
x^2 \times x^5 = x^{2+5} = x^7
\][/tex]
3. Combine the exponents of [tex]\(y\)[/tex]: The expression contains [tex]\(y^3\)[/tex] and [tex]\(y^8\)[/tex]. Similarly, add the exponents together:
[tex]\[
y^3 \times y^8 = y^{3+8} = y^{11}
\][/tex]
Combining all the parts together, the product of the expression is:
[tex]\[
21 x^7 y^{11}
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{21 x^7 y^{11}}
\][/tex]
