Use the properties of rational exponents to simplify $$ \left(\frac{8^{4}}{10^{4}}\right)^{-1 / 4} $$

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To simplify the expression $$ \left(\frac{8^{4}}{10^{4}}\right)^{-1 / 4} $$ using the properties of rational exponents, follow these steps:

1. **Combine the Exponents in the Fraction:**
   
   Notice that both the numerator and the denominator have the same exponent, $$4$$. You can combine them as follows:
   $$
   \frac{8^{4}}{10^{4}} = \left(\frac{8}{10}\right)^{4}
   $$
   
2. **Apply the Outer Exponent:**
   
   Now, apply the exponent $$-\frac{1}{4}$$ to the combined fraction:
   $$
   \left(\left(\frac{8}{10}\right)^{4}\right)^{-\frac{1}{4}} = \left(\frac{8}{10}\right)^{4 \times -\frac{1}{4}} = \left(\frac{8}{10}\right)^{-1}
   $$
   
3. **Simplify the Negative Exponent:**
   
   A negative exponent indicates the reciprocal of the base:
   $$
   \left(\frac{8}{10}\right)^{-1} = \frac{10}{8}
   $$
   
4. **Reduce the Fraction:**
   
   Simplify $$ \frac{10}{8} $$ by dividing both the numerator and the denominator by $$2$$:
   $$
   \frac{10}{8} = \frac{5}{4}
   $$
   
**Final Simplified Form:**
$$
\frac{5}{4}
$$
The simplified form of $$ \left(\frac{8^{4}}{10^{4}}\right)^{-1 / 4} $$ is $$ \frac{5}{4} $$.

Use the properties of rational exponents to simplify

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