To simplify the expression \( \frac{4 \times 10 \times 10 \times 10}{16 \times 10 \times 10} \), we can first cancel out the common terms in the numerator and the denominator.
The expression can be rewritten as:
\[ \frac{4 \times 10^3}{16 \times 10^2} \]
Now, we can simplify the \( 10^2 \) in the denominator with \( 10^3 \) in the numerator:
\[ = \frac{4 \times 10^{3-2}}{16} = \frac{4 \times 10^1}{16} = \frac{40}{16} \]
Next, we can simplify \( \frac{40}{16} \):
\[ = \frac{40 \div 8}{16 \div 8} = \frac{5}{2} \]
Thus, the simplified expression is:
\[ \frac{5}{2} \]
If you wish, this can also be expressed as a decimal:
\[ 2.5 \]
So, the final result is: \[ \frac{5}{2} \text{ or } 2.5 \]