Final answer:
To simplify 9^2 over 9^7, subtract the exponent in the denominator from the numerator which results in 9^(-5). The negative exponent indicates that you should take the reciprocal, so the answer is 1 over 9^5.
Step-by-step explanation:
The question asks to simplify 9^2 over 9^7 as a fraction. When dividing powers with the same base, subtract the exponent in the denominator from the exponent in the numerator. Here, we have 9^2 (which is 9 multiplied by itself twice) divided by 9^7 (which is 9 multiplied by itself seven times).
Using the rule of exponents, we subtract the exponents, which gives us 9^(2-7) = 9^(-5). Now, using the rule that negative exponents indicate division, or flip the construction to the denominator, we rewrite 9^(-5) as 1 over 9^5.
Therefore, the simplified fraction is 1 over 9^5.