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:
\[ 8 \times 10^3 = 40 \times (a \times 10^2) \]
Simplifying the right side:
\[ 8 \times 10^3 = 40a \times 10^2 \]
Next, we can divide both sides by \( 10^2 \):
\[ \frac{8 \times 10^3}{10^2} = 40a \]
This simplifies to:
\[ 8 \times 10^{3-2} = 40a \] \[ 8 \times 10^1 = 40a \]
Now, we can rewrite this as:
\[ 80 = 40a \]
Next, divide both sides by 40 to isolate \( a \):
\[ a = \frac{80}{40} = 2 \]
Thus, the value of \( a \) is:
\[ \boxed{2} \]
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