Certainly! Let's find the product of the expression:
[tex]\[
(3 a^2 b^7)(5 a^3 b^8)
\][/tex]
We will proceed step-by-step to simplify the expression.
Step 1: Multiply the coefficients.
The coefficients in the given expression are [tex]\(3\)[/tex] and [tex]\(5\)[/tex]. Multiplying these gives:
[tex]\[
3 \times 5 = 15
\][/tex]
Step 2: Apply the Laws of Exponents to [tex]\(a\)[/tex] and [tex]\(b\)[/tex].
- For the term involving [tex]\(a\)[/tex]:
[tex]\[
a^2 \times a^3 = a^{2+3} = a^5
\][/tex]
- For the term involving [tex]\(b\)[/tex]:
[tex]\[
b^7 \times b^8 = b^{7+8} = b^{15}
\][/tex]
Step 3: Combine the results from the above steps.
Bringing everything together, we have:
[tex]\[
15 a^5 b^{15}
\][/tex]
Therefore, the product of the expression [tex]\((3 a^2 b^7)(5 a^3 b^8)\)[/tex] is:
[tex]\[
15 a^5 b^{15}
\][/tex]
So the correct answer is:
[tex]\[
\boxed{15 a^5 b^{15}}
\][/tex]
