Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To solve the given problem, we need to multiply the expressions \(3a^2b^7\) and \(5a^3b^8\). We will do this step-by-step, addressing the coefficients, the \(a\) terms, and the \(b\) terms separately.
### Step-by-Step Solution:
1. Multiply the coefficients:
- The coefficients in the expressions are \(3\) and \(5\).
- The product of the coefficients is:
[tex]\[ 3 \times 5 = 15 \][/tex]
2. Multiply the \(a\) terms:
- The exponents of \(a\) in the expressions are \(2\) and \(3\).
- When you multiply terms with the same base, you add their exponents:
[tex]\[ a^2 \times a^3 = a^{2+3} = a^5 \][/tex]
3. Multiply the \(b\) terms:
- The exponents of \(b\) in the expressions are \(7\) and \(8\).
- Similarly, when you multiply terms with the same base, you add their exponents:
[tex]\[ b^7 \times b^8 = b^{7+8} = b^{15} \][/tex]
### Putting it all together:
Combining the results from each step, the product of the expressions \(3a^2b^7\) and \(5a^3b^8\) is:
[tex]\[ 15 a^5 b^{15} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{15 a^5 b^{15}} \][/tex]
### Step-by-Step Solution:
1. Multiply the coefficients:
- The coefficients in the expressions are \(3\) and \(5\).
- The product of the coefficients is:
[tex]\[ 3 \times 5 = 15 \][/tex]
2. Multiply the \(a\) terms:
- The exponents of \(a\) in the expressions are \(2\) and \(3\).
- When you multiply terms with the same base, you add their exponents:
[tex]\[ a^2 \times a^3 = a^{2+3} = a^5 \][/tex]
3. Multiply the \(b\) terms:
- The exponents of \(b\) in the expressions are \(7\) and \(8\).
- Similarly, when you multiply terms with the same base, you add their exponents:
[tex]\[ b^7 \times b^8 = b^{7+8} = b^{15} \][/tex]
### Putting it all together:
Combining the results from each step, the product of the expressions \(3a^2b^7\) and \(5a^3b^8\) is:
[tex]\[ 15 a^5 b^{15} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{15 a^5 b^{15}} \][/tex]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.