2^2/3/2000^2/3
You asked:
Evaluate the expression: \(\frac{\frac{\frac{{2}^{2}}{3}}{{2000}^{2}}}{3}\)
MathBot Answer:
\[\frac{\frac{\frac{{2}^{2}}{3}}{{2000}^{2}}}{3} = \frac{1}{9000000} = 0.000000\overline{1}\]
\[\begin{aligned}\frac{\frac{\frac{{2}^{2}}{3}}{{2000}^{2}}}{3}& = 2^{2} \cdot \frac{1}{3} \cdot \frac{1}{2000^{2}} \cdot \frac{1}{3}\\& = \frac{4}{3} \cdot \frac{1}{2000^{2}} \cdot \frac{1}{3}\\& = \frac{4}{3} \cdot \frac{1}{4000000} \cdot \frac{1}{3}\\& = \frac{4}{3} \cdot \frac{1}{12000000}\\& = \frac{1}{9000000}\end{aligned}\]