To find the value of \( a \) such that \( 8 \times 10^3 \) is 40 times larger than \( a \times 10^2 \), we can set up the equation:
\[ 8 \times 10^3 = 40 \times (a \times 10^2) \]
Now, we can simplify the right side:
\[ 8 \times 10^3 = 40a \times 10^2 \]
Next, we can divide both sides of the equation by \( 10^2 \):
\[ \frac{8 \times 10^3}{10^2} = 40a \]
This simplifies to:
\[ 8 \times 10^{3-2} = 40a \]
\[ 8 \times 10^1 = 40a \]
This gives us:
\[ 80 = 40a \]
Now, to solve for \( a \), we divide both sides by 40:
\[ a = \frac{80}{40} \]
\[ a = 2 \]
Thus, the value of \( a \) is \( 2 \).