Answer :
To solve the problem of multiplying [tex]\(4x^4 \cdot 2x^9\)[/tex] using the product rule, follow these steps:
1. Multiply the coefficients: The coefficients in the terms are 4 and 2. When you multiply these two coefficients together, you get:
[tex]\[
4 \times 2 = 8
\][/tex]
2. Apply the product rule for exponents: When multiplying terms with the same base, you add the exponents. Here, both terms have the base [tex]\(x\)[/tex] with exponents 4 and 9, respectively. Therefore, you add the exponents:
[tex]\[
4 + 9 = 13
\][/tex]
3. Combine the results: After multiplying the coefficients and adding the exponents, you combine these to get the final expression:
[tex]\[
8x^{13}
\][/tex]
So, the product of [tex]\(4x^4 \cdot 2x^9\)[/tex] is [tex]\(8x^{13}\)[/tex].
1. Multiply the coefficients: The coefficients in the terms are 4 and 2. When you multiply these two coefficients together, you get:
[tex]\[
4 \times 2 = 8
\][/tex]
2. Apply the product rule for exponents: When multiplying terms with the same base, you add the exponents. Here, both terms have the base [tex]\(x\)[/tex] with exponents 4 and 9, respectively. Therefore, you add the exponents:
[tex]\[
4 + 9 = 13
\][/tex]
3. Combine the results: After multiplying the coefficients and adding the exponents, you combine these to get the final expression:
[tex]\[
8x^{13}
\][/tex]
So, the product of [tex]\(4x^4 \cdot 2x^9\)[/tex] is [tex]\(8x^{13}\)[/tex].
