To simplify the expression [tex]\(\left(2 x^2\right)\left(3 x^3\right)\)[/tex], let's go through it step-by-step.
1. Separate the Constants and Variable Parts:
- We have the constants [tex]\(2\)[/tex] and [tex]\(3\)[/tex].
- We have the variable parts [tex]\(x^2\)[/tex] and [tex]\(x^3\)[/tex].
2. Multiply the Constants:
- Multiply the constants: [tex]\(2\)[/tex] and [tex]\(3\)[/tex].
[tex]\[
2 \cdot 3 = 6
\][/tex]
3. Apply the Property of Exponents:
- When multiplying two expressions with the same base, you add the exponents: [tex]\(x^a \cdot x^b = x^{a+b}\)[/tex].
- Here, [tex]\(x^2 \cdot x^3\)[/tex]:
[tex]\[
x^{2+3} = x^5
\][/tex]
4. Combine the Results:
- Combine the product of the constants with the simplified exponent:
[tex]\[
6 \cdot x^5 = 6x^5
\][/tex]
So, the simplified expression is [tex]\(6x^5\)[/tex]. Therefore, the correct answer is:
[tex]\(\boxed{6 x^5}\)[/tex]
