Answer :

Sure! Let's simplify the expression [tex]\(\left(2 x^5 y^2\right)\left(3 x^3 y\right)\)[/tex] step-by-step.

1. Distribute the coefficients:
- Multiply the coefficients 2 and 3:
[tex]\[ 2 \cdot 3 = 6 \][/tex]

2. Distribute the [tex]\(x\)[/tex] terms:
- For [tex]\(x^5\)[/tex] and [tex]\(x^3\)[/tex], use the property of exponents that states [tex]\(a^m \cdot a^n = a^{m+n}\)[/tex]:
[tex]\[ x^5 \cdot x^3 = x^{5+3} = x^8 \][/tex]

3. Distribute the [tex]\(y\)[/tex] terms:
- For [tex]\(y^2\)[/tex] and [tex]\(y\)[/tex], use the property of exponents:
[tex]\[ y^2 \cdot y = y^{2+1} = y^3 \][/tex]

Putting it all together, we get:
[tex]\[ 6 \cdot x^8 \cdot y^3 \][/tex]

Therefore, the simplified expression is:
[tex]\[ 6 x^8 y^3 \][/tex]

Thus, the correct answer is: [tex]\(\boxed{6 x^8 y^3}\)[/tex]