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To determine who has more money in their account, we need to evaluate the given expressions:
Sama's account: $5^8⋅^54/(5^3)^2
Evaluating this expression:
$5^8 = $390,625
$^54 = $625
(5^3)^2 = 5^6 = $15,625
Therefore, Sama has $390,625⋅$625/$15,625 = $15,625 in their account.
Jimena's account: $2^9⋅(2^−2)^−3/2
Evaluating this expression:
$2^9 = $512
(2^−2)^−3 = (1/2^2)^−3 = (1/4)^−3 = 4^3 = 64
64/2 = $32
Therefore, Jimena has $512⋅$32 = $16,384 in their account.
Comparing the two amounts, we can see that Sama has more money in their account.
The difference in the amount of money that they have is:
$15,625 - $16,384 = -$759
Therefore, Jimena has $759 less in their account compared to Sama.