Question

Simplify 9^2 over 9^7

Answer 1

1/59049 !!!!!!!!!!!!!!!!!!!!

Answer 2

`\( (9^2)/(9^7) \)` simplifies to
`\(9^(-5)\)`, representing the reciprocal of
`\(9^5\)`. This follows the rule
`\(a^m / a^n = a^(m-n)\)`, showcasing the exponent subtraction when dividing powers of the same base.

To simplify
`\((9^2)/(9^7)\)`, apply the rule
`\(a^m / a^n = a^(m-n)\)` for the same base a. In this case, both bases are 9.

`\[(9^2)/(9^7) = 9^(2-7) = 9^(-5)\]`

So,
`\((9^2)/(9^7) = (1)/(9^5)\)` or
`\(9^(-5)\)`.

The expression
`\( (9^2)/(9^7) \)` simplifies to
`\( 9^(-5) \)` using the rule
`\(a^m / a^n = a^(m-n)\)`. This simplification represents the reciprocal of
`\(9^5\)`, emphasizing the inverse relationship between the numerator and denominator.

Thus, the result is a fraction with the base 9 raised to the power of -5, indicating that the expression is equivalent to
`\( (1)/(9^5) \)`. This showcases the mathematical principle of exponent subtraction when dividing powers of the same base, resulting in a concise and simplified form for the given expression.