Questions: =37/((1/5)^2+(-5/6)^-2)

Solution Steps

We start by calculating \( \left(\frac{1}{5}\right)^2 \): \[ \left(\frac{1}{5}\right)^2 = \frac{1^2}{5^2} = \frac{1}{25} \] After simplification, we find: \[ \text{Simplified } \left(\frac{1}{5}\right)^2 = 25 \]

Next, we simplify \( \left(-\frac{5}{6}\right)^{-2} \): \[ \left(-\frac{5}{6}\right)^{-2} = \left(\frac{6}{-5}\right)^2 = \frac{6^2}{(-5)^2} = \frac{36}{25} \] After simplification, we find: \[ \text{Simplified } \left(-\frac{5}{6}\right)^{-2} = 900 \]

Now, we add the results from Step 1 and Step 2: \[ \frac{1}{25} + \frac{36}{25} = \frac{1 + 36}{25} = \frac{37}{25} \] After simplification, we find: \[ \text{Sum of } \left(\frac{1}{5}\right)^2 \text{ and } \left(-\frac{5}{6}\right)^{-2} = 22500 \]

Finally, we divide 37 by the result from Step 3: \[ \frac{37}{\frac{37}{25}} = 37 \times \frac{25}{37} = 25 \] After simplification, we find: \[ \text{Final result} = 832500 \]

Final Answer