Step 1 :Simplify the expression: \(\frac{2 a^{6} b^{2} c}{10 a^{2} b^{-2} c}\)
Step 2 :Combine like terms: \(\frac{2 a^{6-2} b^{2-(-2)}}{10}\)
Step 3 :Simplify the exponents: \(\frac{2 a^{4} b^{4}}{10}\)
Step 4 :Divide the coefficients: \(\frac{a^{4} b^{4}}{5}\)
Step 5 :Final Answer: \(\boxed{\frac{a^{4} b^{4}}{5}}\)