To determine which expression is equivalent to [tex]\(\frac{60 x^{20} y^{24}}{30 x^{10} y^{12}}\)[/tex], let's break down the components and simplify step by step.
1. Simplify the Coefficients:
[tex]\[
\frac{60}{30} = 2
\][/tex]
2. Simplify the [tex]\(x\)[/tex] Term:
[tex]\[
\frac{x^{20}}{x^{10}} = x^{20 - 10} = x^{10}
\][/tex]
3. Simplify the [tex]\(y\)[/tex] Term:
[tex]\[
\frac{y^{24}}{y^{12}} = y^{24 - 12} = y^{12}
\][/tex]
Combining these simplified components, the equivalent expression is:
[tex]\[
2 x^{10} y^{12}
\][/tex]
Therefore, the expression equivalent to [tex]\(\frac{60 x^{20} y^{24}}{30 x^{10} y^{12}}\)[/tex] is:
[tex]\[
\boxed{2 x^{10} y^{12}}
\][/tex]
