1 ÷ √(50 × 10^-3 × 80 × 10^-6)
You asked:
Evaluate the expression: \(\frac{1}{\sqrt{50 \cdot {10}^{-3} \cdot 80 \cdot {10}^{-6}}}\)
MathBot Answer:
\[\frac{1}{\sqrt{50 \cdot {10}^{-3} \cdot 80 \cdot {10}^{-6}}} = 500\]
\[\begin{aligned}\frac{1}{\sqrt{50 \cdot {10}^{-3} \cdot 80 \cdot {10}^{-6}}}& = \frac{1}{\sqrt{50 \cdot \frac{1}{10^{3}} \cdot 80 \cdot \frac{1}{10^{6}}}}\\& = \frac{1}{\sqrt{\frac{50}{1000} \cdot 80 \cdot \frac{1}{10^{6}}}}\\& = \frac{1}{\sqrt{\frac{50}{1000} \cdot \frac{80}{1000000}}}\\& = \frac{1}{\sqrt{\frac{80}{20} \cdot \frac{1}{1000000}}}\\& = \frac{1}{\sqrt{\frac{4}{1000000}}}\\& = \frac{1}{\sqrt{\frac{1}{250000}}}\\& = \frac{1}{\frac{1}{500}}\\& = 500\end{aligned}\]