Answer :
To solve the expression [tex]\(3x^5 \cdot 7x^9\)[/tex], we need to follow these steps:
1. Multiply the Coefficients:
- The coefficients are the numerical parts of the terms, which are 3 and 7 in this case.
- Multiply these coefficients: [tex]\(3 \times 7 = 21\)[/tex].
2. Add the Exponents:
- When multiplying terms with the same base (in this case, [tex]\(x\)[/tex]), you can add the exponents.
- The exponents here are 5 and 9.
- Add these exponents: [tex]\(5 + 9 = 14\)[/tex].
3. Combine the Results:
- Now put the new coefficient and the sum of the exponents together: [tex]\(21x^{14}\)[/tex].
Therefore, the expression [tex]\(3x^5 \cdot 7x^9\)[/tex] is equivalent to [tex]\(21x^{14}\)[/tex].
The correct answer is choice J: [tex]\(21x^{14}\)[/tex].
1. Multiply the Coefficients:
- The coefficients are the numerical parts of the terms, which are 3 and 7 in this case.
- Multiply these coefficients: [tex]\(3 \times 7 = 21\)[/tex].
2. Add the Exponents:
- When multiplying terms with the same base (in this case, [tex]\(x\)[/tex]), you can add the exponents.
- The exponents here are 5 and 9.
- Add these exponents: [tex]\(5 + 9 = 14\)[/tex].
3. Combine the Results:
- Now put the new coefficient and the sum of the exponents together: [tex]\(21x^{14}\)[/tex].
Therefore, the expression [tex]\(3x^5 \cdot 7x^9\)[/tex] is equivalent to [tex]\(21x^{14}\)[/tex].
The correct answer is choice J: [tex]\(21x^{14}\)[/tex].
