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Simplify 9^2 over 9^7 as a fraction:

a) 9^5
b) 1 over 9^9
c) 1 over 9^-5
d) 1 over 9^5

User StiGMaT
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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.

User Martidis
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