Solve (10/13)^(-4): Negative Exponent Calculation

Insert the corresponding expression:

$\left(\frac{10}{13}\right)^{-4}=$

To solve the expression $\left(\frac{10}{13}\right)^{-4}$, we start by applying the rule for dividing exponents is:

$\frac{10^{-4}}{13^{-4}}$, which maintains the negative exponent but as separate components of fraction resulting in the same value.

Consequently, the expression $\left(\frac{10}{13}\right)^{-4}$ equates to $\frac{10^{-4}}{13^{-4}}$.

By comparing this with the presented choices, we identify that option (2):

$\frac{10^{-4}}{13^{-4}}$

matches correctly with our conversion of the original expression.

Therefore, the correct expression is $\frac{10^{-4}}{13^{-4}}$.