To determine which expression is equivalent to [tex]\(\frac{10 a^{10}}{2 a^2}\)[/tex], we can simplify the given fraction step by step. Let's proceed with the simplification:
1. Simplify the coefficients:
- The numerator has a coefficient of 10.
- The denominator has a coefficient of 2.
- When we divide 10 by 2, we get 5.
Therefore, the simplified coefficient is 5.
2. Simplify the exponent of [tex]\( a \)[/tex]:
- The numerator has [tex]\( a^{10} \)[/tex].
- The denominator has [tex]\( a^2 \)[/tex].
- When we divide powers of the same base, we subtract the exponents (i.e., [tex]\( a^m / a^n = a^{m-n} \)[/tex]).
So, [tex]\( a^{10} / a^2 = a^{10-2} = a^8 \)[/tex].
Combining these two results, the simplified expression for [tex]\(\frac{10 a^{10}}{2 a^2}\)[/tex] is:
[tex]\[
5 a^8
\][/tex]
### Answer:
The equivalent expression to [tex]\(\frac{10 a^{10}}{2 a^2}\)[/tex] is:
[tex]\[ 5 a^8 \][/tex]
Thus, the correct choice from the provided options is:
[tex]\[ \boxed{5 a^8} \][/tex]
