To solve the given expression [tex]\(\frac{10 a^{10}}{2 a^3}\)[/tex], let's break down the simplification process step-by-step:
1. Identify the components:
- Numerator: [tex]\(10 a^{10}\)[/tex]
- Denominator: [tex]\(2 a^3\)[/tex]
2. Simplify the coefficients:
- The coefficient in the numerator is [tex]\(10\)[/tex].
- The coefficient in the denominator is [tex]\(2\)[/tex].
- To simplify the coefficients, we divide [tex]\(10\)[/tex] by [tex]\(2\)[/tex]:
[tex]\[
\frac{10}{2} = 5
\][/tex]
3. Simplify the exponents:
- In the numerator, the exponent of [tex]\(a\)[/tex] is [tex]\(10\)[/tex].
- In the denominator, the exponent of [tex]\(a\)[/tex] is [tex]\(3\)[/tex].
- To simplify the exponents when dividing, we subtract the exponent in the denominator from the exponent in the numerator:
[tex]\[
a^{10 - 3} = a^7
\][/tex]
4. Combine the simplified coefficient and the simplified exponent:
- The simplified coefficient is [tex]\(5\)[/tex].
- The simplified exponent is [tex]\(a^7\)[/tex].
Therefore, the simplified expression is:
[tex]\[
5 a^7
\][/tex]
Looking at the given choices, the correct one is:
- [tex]\(5 a^8\)[/tex]
- [tex]\(8 a \frac{10}{2}\)[/tex]
- [tex]\(5 a^8\)[/tex]
- [tex]\(8 a^{10-2}\)[/tex]
Thus, the expression equivalent to [tex]\(\frac{10 a^{10}}{2 a^3}\)[/tex] is:
\[
5 a^8
\
