Option C:
[tex]\left(7 x^{2} y^{3}\right)\left(3 x^{5} y^{8}\right)=21 x^{7} y^{11}[/tex]
Solution:
Given expression is [tex]\left(7 x^{2} y^{3}\right)\left(3 x^{5} y^{8}\right)[/tex].
To find the product of the above expression.
[tex]\left(7 x^{2} y^{3}\right)\left(3 x^{5} y^{8}\right)[/tex]
First multiply the numerical coefficients.
[tex]\left(7 x^{2} y^{3}\right)\left(3 x^{5} y^{8}\right)=21 x^{2} y^{3} x^{5} y^{8}[/tex]
Arrange the terms with same base.
[tex]=21 x^{2} x^{5} y^{3} y^{8}[/tex]
Using exponent rule: [tex]a^m \cdot a^n = a^{m+n}[/tex]
[tex]=21 x^{2+5} y^{3+8}[/tex]
[tex]=21 x^{7} y^{11}[/tex]
[tex]\left(7 x^{2} y^{3}\right)\left(3 x^{5} y^{8}\right)=21 x^{7} y^{11}[/tex]
Hence option C is the correct answer.
