To find the product of \(\left(3 a^2 b^7\right) \left(5 a^3 b^8\right)\), let's break down the multiplication step by step:
1. Multiply the coefficients:
The coefficients are the numerical parts of each term. Here, the coefficients are 3 and 5.
[tex]\[
3 \times 5 = 15
\][/tex]
2. Add the exponents of \(a\):
The exponents of \(a\) in the terms are 2 and 3 respectively.
[tex]\[
a^{2+3} = a^5
\][/tex]
3. Add the exponents of \(b\):
The exponents of \(b\) in the terms are 7 and 8 respectively.
[tex]\[
b^{7+8} = b^{15}
\][/tex]
Combining these results, we get:
[tex]\[
15 \cdot a^5 \cdot b^{15}
\][/tex]
So the product is:
[tex]\[
15 a^5 b^{15}
\][/tex]
Thus, the correct answer is:
[tex]\[
15 a^5 b^{15}
\][/tex]
