To simplify the given expression \( x^{-7} \times y^{77} \):
1. Understand the properties of exponents:
- The negative exponent rule states that \( a^{-n} = \frac{1}{a^n} \).
2. Apply the negative exponent rule to the term \( x^{-7} \):
- \( x^{-7} = \frac{1}{x^7} \).
3. Now rewrite the given expression using this rule:
- \( x^{-7} \times y^{77} = \frac{1}{x^7} \times y^{77} \).
4. Combining the terms in a single fraction, the expression becomes:
- \( \frac{y^{77}}{x^7} \).
Therefore, the simplified form of the expression \( x^{-7} \times y^{77} \) is:
[tex]\[
\boxed{\frac{y^{77}}{x^7}}
\][/tex]
