Given: 125\(^{−\frac{1}{3}}\) × 49\(^{−\frac{1}{2}}\) × 10\(^0\)

125\(^{-1/3}\) = (5\(^3\))\(^{-1/3}\) = 5\(^{-1}\) = \(\frac{1}{5}\).

49\(^{-1/2}\) = (7\(^2\))\(^{-1/2}\) = 7\(^{-1}\) = \(\frac{1}{7}\).

10\(^0\) = 1.

Product = \(\frac{1}{5}\) x \(\frac{1}{7}\) x 1 = \(\frac{1}{35}\).