The solution set for the given inequality is 
<u>Given the following inequality:</u>
<h3>What is an inequality?</h3>
An inequality can be defined as a mathematical relation that is typically used to compare two (2) integers or variables in an equation by illustrating any of the following:
- Greater than or equal to the other (≥).
- Less than or equal to the other (≤).
Simplifying the inequality, we have:

Read more on inequality here: brainly.com/question/24372553
When you multiply a same number but with different powers, you can simply add the powers together. So, in your question, add the powers -1 and -7 together.
7^(-1) x 7^(-7) = 7^(-8)
When you divide a same number but with different powers, you subtract the power at the top with the power from the denominator. So, -8 - (-7) = -1.
7^(-8) / 7^(-7) = 7^(-1)
So your answer would be 7^(-1).
Hopefully my explanation was clear?