To determine the product of the given expression [tex]\((3 a^2 b^7)(5 a^3 b^8)\)[/tex], let's break it down step by step.
1. Multiply the Coefficients:
- The coefficient of the first term is 3.
- The coefficient of the second term is 5.
- Multiply the coefficients: [tex]\(3 \times 5 = 15\)[/tex].
2. Combine the Exponents of 'a':
- For [tex]\(a\)[/tex], the exponent in the first term is 2.
- The exponent in the second term is 3.
- Add the exponents together: [tex]\(2 + 3 = 5\)[/tex].
3. Combine the Exponents of 'b':
- For [tex]\(b\)[/tex], the exponent in the first term is 7.
- The exponent in the second term is 8.
- Add the exponents together: [tex]\(7 + 8 = 15\)[/tex].
Putting it all together, the product of the expression is:
[tex]\[ 15 a^5 b^{15} \][/tex]
Thus, the correct answer is:
[tex]\[ 15 a^5 b^{15} \][/tex]
