UNDRAISERS The hospital spent \( 9^{5} \) dollars on new medical equipment this year. Last ear, they spent \( 9^{7} \) dollars. How many times more money did they spend last year than his year? IEASUREMENT 1 milligram is equal to \( 10^{-3} \) grams. Write this number using a positive xponent.
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The hospital spent \( 9^7 \) dollars last year and \( 9^5 \) dollars this year. To find how many times more was spent last year, we can divide the two amounts: \[ \frac{9^7}{9^5} = 9^{7-5} = 9^2 = 81. \] So, they spent 81 times more last year compared to this year! Now, regarding milligrams and grams, since \( 1 \text{ mg} = 10^{-3} \text{ g} \), we want to express \( 10^{-3} \) with a positive exponent. The equivalent positive exponent form is \( \frac{1}{10^3} \) or \( 10^3 = 1000 \). But if we refer to the mass in milligrams, we can also say that 1000 milligrams make up 1 gram, maintaining that relationship with a positive focus!
