lim _(xarrow 0)(1-5x)^(2)/(3/n)x=

To evaluate the limit \(\lim_{x \to 0} (1 - 5x)^{\frac{2}{3/n}x}\), we can use the exponential function and properties of limits.First, let's rewrite the expression in a more convenient form. We have: We can express this using the exponential function : Now, we need to evaluate the limit of the exponent: As , , and \(\ln(1 - 5x) \to \ln(1) = 0\). Therefore, we have: So, the expression simplifies to: Therefore, the limit is: