Question: Simplify.
$\frac{5y^{12}}{10y^{5}}$
A $\frac{y^{17}}{2}$
B $2y^{7}$
C $\frac{y^{7}}{2}$
D $2y^{17}$
1. **State the problem:** Simplify the expression $$\frac{5y^{12}}{10y^{5}}$$.
2. **Recall the rules:** When dividing terms with the same base, subtract the exponents: $$\frac{a^{m}}{a^{n}} = a^{m-n}$$.
3. **Simplify the coefficients:** $$\frac{5}{10} = \frac{\cancel{5}}{2\times\cancel{5}} = \frac{1}{2}$$.
4. **Simplify the variables:** $$y^{12} \div y^{5} = y^{12-5} = y^{7}$$.
5. **Combine the simplified parts:** $$\frac{1}{2} \times y^{7} = \frac{y^{7}}{2}$$.
6. **Final answer:** The simplified expression is $$\frac{y^{7}}{2}$$, which corresponds to option C.