two students have bank accounts: sama: $ 5^8⋅5^4 /(5^3)^2 jimena: $ 2^9⋅(2^−2)^−3/2 (4 points) who has more money in their account? what is the difference in the amount of money that they have? 0 difference in their accounts, 7 times more money, they both have the same amount of money. $759, $523, $1000

1 answer

To determine who has more money in their account, we need to simplify the expressions for Sama and Jimena's accounts.

For Sama:
$5^8⋅5^4 /(5^3)^2
= 5^(8+4) / 5^6
= 5^12 / 5^6
= 5^(12-6)
= 5^6
= 15625

For Jimena:
$2^9⋅(2^−2)^−3/2
= 2^9 * 2^(6/2)
= 2^(9+3)
= 2^12
= 4096

Therefore, Sama has $15625 in her account, while Jimena has $4096 in her account. The difference in the amount of money that they have is $11529. So, the correct answer is $11529.
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