At a mountain adventure camp, Emek and Tara had to activate three emergency signal stations before the expedition began. Each station accepted only a value matching its numerical requirement. The first required a rational number equal to 2.25, so they selected 9/4 from the control panel. The second required an exact irrational value between 4 and 5. Tara compared sqrt(19) with nearby perfect squares: sqrt(16) was 4 and sqrt(25) was 5, so sqrt(19) fit the requirement. At the final station, the display showed 2^6 divided by 2^2. Emek used the exponent rule to simplify it to 2^4, or 16, rather than calculating each power separately. They checked that 16 was an integer, rational number, and real number. With all three values confirmed in exact form, the final station flashed green. A signal traveled from peak to peak, activating the entire emergency network before the expedition set out.