College

What is [tex]$4x^3$[/tex] times [tex]$5x^9$[/tex]?

A. [tex]$20x^{27}$[/tex]
B. [tex]$20x^{12}$[/tex]
C. [tex]$9x^{27}$[/tex]
D. [tex]$9x^{12}$[/tex]

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].