Two students have bank accounts:
Sama: $ (5^(8)*5^(4))/((5^(3))^(2))
Jimena: $ (2^(9)*(2^(-2))^(-3))/(2)
Who has more money in their account?
What is the difference in the amount of money that they have?
Word bank:
$523
7 times more money
$1000
Jimena
They both have the same amount of money.
Sama
0 difference in the accounts
$759
To solve this problem, we need to simplify the expressions for each student's bank account and compare them.
Sama's bank account can be simplified as follows:
(5^8 * 5^4) / ((5^3)^2)
= (5^12) / (5^6)
= 5^(12-6)
= 5^6
Jimena's bank account can be simplified as follows:
(2^9 * (2^(-2))^(-3)) / 2
= (2^9 * 2^(6)) / 2
= 2^(9+6)
= 2^15
Comparing the simplified expressions, we can see that Sama's account has 5^6, while Jimena's account has 2^15. Since 5^6 is not equal to 2^15, we can conclude that they both do not have the same amount of money.
To find out who has more money, we need to compare the values of 5^6 and 2^15.
5^6 = 5 * 5 * 5 * 5 * 5 * 5 = 15625
2^15 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 32768
Since 32768 is greater than 15625, Jimena has more money in her account than Sama.
To find the difference in the amount of money, we can subtract the smaller amount from the larger amount:
32768 - 15625 = 17143
Therefore, Jimena has $17,143 more in her account than Sama.