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What is the length of an with endpoints a 3,2 and b 8,14

Trent wants to buy 2 packs of trading cards for 3 dollars each. the trading card packs that trent normally buys tend to come in packs of 6, 10, 12, or 15 cards. after selecting 2 packs, trent found that the first pack of cards cost 25 cents per card, and the second pack cost 30 cents per card. trent uses this information to write the equations below in order to compare c, the number of cards in each pack.

Elizabeth claims that the fourth root of 2 can be expressed as 2^m since (2^m)^n = 2. find the values of m and n for the case where elizabeth's claim is true.