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Answer :
To solve the problem of multiplying [tex]\(4x^3\)[/tex] by [tex]\(5x^9\)[/tex], let's go through the steps:
1. Multiply the Coefficients:
- The coefficients are the numerical parts in front of the variable [tex]\(x\)[/tex].
- For [tex]\(4x^3\)[/tex] and [tex]\(5x^9\)[/tex], the coefficients are 4 and 5.
- Multiply these together: [tex]\(4 \times 5 = 20\)[/tex].
2. Add the Exponents:
- The base of the exponents is the same for both terms, which is [tex]\(x\)[/tex].
- When you multiply terms with the same base, you add the exponents.
- Here, the exponents are 3 and 9 for [tex]\(x^3\)[/tex] and [tex]\(x^9\)[/tex], respectively.
- Add these exponents: [tex]\(3 + 9 = 12\)[/tex].
3. Write the Result:
- Combine the result of the coefficients and the exponents to form the final expression.
- So, [tex]\(4x^3 \times 5x^9 = 20x^{12}\)[/tex].
Hence, the answer is [tex]\(20x^{12}\)[/tex].
1. Multiply the Coefficients:
- The coefficients are the numerical parts in front of the variable [tex]\(x\)[/tex].
- For [tex]\(4x^3\)[/tex] and [tex]\(5x^9\)[/tex], the coefficients are 4 and 5.
- Multiply these together: [tex]\(4 \times 5 = 20\)[/tex].
2. Add the Exponents:
- The base of the exponents is the same for both terms, which is [tex]\(x\)[/tex].
- When you multiply terms with the same base, you add the exponents.
- Here, the exponents are 3 and 9 for [tex]\(x^3\)[/tex] and [tex]\(x^9\)[/tex], respectively.
- Add these exponents: [tex]\(3 + 9 = 12\)[/tex].
3. Write the Result:
- Combine the result of the coefficients and the exponents to form the final expression.
- So, [tex]\(4x^3 \times 5x^9 = 20x^{12}\)[/tex].
Hence, the answer is [tex]\(20x^{12}\)[/tex].
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