To determine 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, let's simplify the right side of the equation:
\[ 8 \times 10^3 = 40a \times 10^2 \]
Next, we can divide both sides by \( 10^2 \) to make it easier to solve for \( a \):
\[ \frac{8 \times 10^3}{10^2} = 40a \]
Simplifying the left side yields:
\[ 8 \times 10^{3-2} = 40a \] \[ 8 \times 10^1 = 40a \] \[ 80 = 40a \]
Next, we can solve for \( a \) by dividing both sides by 40:
\[ a = \frac{80}{40} = 2 \]
Thus, the value of \( a \) is \( 2 \).