(1/2).10^8 . 5 . (1/4)^3

To simplify the expression \( \frac{1}{2} \cdot 10^8 \cdot 5 \cdot \left(\frac{1}{4}\right)^3 \):

1. Calculate \( \left(\frac{1}{4}\right)^3 \):
\[
\left(\frac{1}{4}\right)^3 = \frac{1^3}{4^3} = \frac{1}{64}
\]

2. Substitute into the expression:
\[
\frac{1}{2} \cdot 10^8 \cdot 5 \cdot \frac{1}{64}
\]

3. Multiply the constants:
\[
\frac{1}{2} \cdot 5 = \frac{5}{2}
\]

4. Now multiply by \( 10^8 \):
\[
\frac{5}{2} \cdot 10^8 = \frac{5 \cdot 10^8}{2}
\]

5. Finally, divide by 64:
\[
\frac{5 \cdot 10^8}{2 \cdot 64} = \frac{5 \cdot 10^8}{128}
\]

To calculate \( \frac{5 \cdot 10^8}{128} \):
\[
= 3.90625 \times 10^6
\]

So, the simplified result is:
\[
3.90625 \times 10^6
\]

Let me know if you need any further calculations or clarifications!