To simplify the expression [tex]\(\frac{60 x^{20} y^{24}}{30 x^{10} y^{12}} \)[/tex], follow these steps:
1. Simplify the coefficients:
- The coefficient in the numerator is [tex]\(60\)[/tex].
- The coefficient in the denominator is [tex]\(30\)[/tex].
- Divide the coefficients: [tex]\(\frac{60}{30} = 2\)[/tex].
2. Simplify the powers of [tex]\(x\)[/tex]:
- The power of [tex]\(x\)[/tex] in the numerator is [tex]\(20\)[/tex].
- The power of [tex]\(x\)[/tex] in the denominator is [tex]\(10\)[/tex].
- Subtract the powers: [tex]\(20 - 10 = 10\)[/tex].
- So, [tex]\(x^{20} / x^{10} = x^{10}\)[/tex].
3. Simplify the powers of [tex]\(y\)[/tex]:
- The power of [tex]\(y\)[/tex] in the numerator is [tex]\(24\)[/tex].
- The power of [tex]\(y\)[/tex] in the denominator is [tex]\(12\)[/tex].
- Subtract the powers: [tex]\(24 - 12 = 12\)[/tex].
- So, [tex]\(y^{24} / y^{12} = y^{12}\)[/tex].
Combining all these simplified parts, we get:
[tex]\[
\frac{60 x^{20} y^{24}}{30 x^{10} y^{12}} = 2 x^{10} y^{12}
\][/tex]
Thus, the expression equivalent to [tex]\(\frac{60 x^{20} y^{24}}{30 x^{10} y^{12}} \)[/tex] is:
[tex]\[
2 x^{10} y^{12}
\][/tex]
The correct choice among the given options is [tex]\(2 x^{10} y^{12}\)[/tex].
