Simplify 9 to the 2nd over 9 to the 7th.
Answer:
The simplified form of \(\frac{9^2}{9^7}\) is \(\frac{1}{9^5}\).
Step-by-step explanation:
Consider the provided information.
9 to the 2nd over 9 to the 7th
This can be written as:
\(\frac{9^2}{9^7}\)
Use the quotient rule of exponent:
\(\frac{a^m}{a^n}=a^{m-n}\)
By using the above rule.
\(9^{2-7}\)
\(9^{-5}\)
Now use the negative exponent rule: \(a^{-n}=\frac{1}{a^n}\)
By using the above rule:
\(9^{-5}=\frac{1}{9^5}\)
Hence, the simplified form of \(\frac{9^2}{9^7}\) is \(\frac{1}{9^5}\).