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]
