We can evaluate \((343)^{\frac{1}{3}} \times (0.14)^{-1} \times (25)^{-\frac{1}{2}}\) without using tables by breaking down each part of the expression:

- \((343)^{\frac{1}{3}}\) is the cube root of 343, which is 7.

- \((0.14)^{-1}\) is the reciprocal of 0.14, which is \(\frac{1}{0.14}\). This can be simplified to \(\frac{10}{1.4}\), which is approximately 7.14.

- \((25)^{-\frac{1}{2}}\) is the reciprocal of the square root of 25, which is \(\frac{1}{5}\).

Multiplying all these values together, we get:

\(7 \times 7.14 \times \frac{1}{5} = 10\)

So the value of the expression is 10.