To determine which option matches the given expression, let's go through a step-by-step solution.
The expression given is:
[tex]\[
\frac{a^2}{5} \cdot 10
\][/tex]
First, we need to simplify this expression.
1. Start with the multiplication inside the expression:
[tex]\[
\frac{a^2}{5} \times 10
\][/tex]
2. Multiply the numerator (the part of the fraction that is above the line) by 10:
[tex]\[
\frac{a^2 \times 10}{5}
\][/tex]
3. Simplify the fraction by dividing the numerator by the denominator:
[tex]\[
\frac{10a^2}{5}
\][/tex]
4. Perform the division:
[tex]\[
10a^2 \div 5 = 2a^2
\][/tex]
Thus, the simplified product is:
[tex]\[
2a^2
\][/tex]
Now, we compare this simplified product with the given options:
1. [tex]\(2a^2\)[/tex]
2. [tex]\(5a^2\)[/tex]
3. [tex]\(\left(\frac{a}{2}\right)^2\)[/tex]
4. [tex]\(\left(\frac{a}{5}\right)^2\)[/tex]
It's clear that the simplified expression [tex]\(2a^2\)[/tex] matches the first option.
Therefore, the correct option is:
2a^2, which corresponds to option 1.
