Two students have bank accounts:Sama: $ 5^8⋅^54/(5^3)^2Jimena: $2^9⋅(2^−2)^−3/2 Two students have bank accounts:%0D%0A%0D%0ASama: $ 58⋅54(53)2%0D%0A5%0D%0A8%0D%0A⋅%0D%0A5%0D%0A4%0D%0A(%0D%0A5%0D%0A3%0D%0A)%0D%0A2%0D%0A %0D%0AJimena: $29⋅(2−2)−32%0D%0A2%0D%0A9%0D%0A⋅%0D%0A(%0D%0A2%0D%0A−%0D%0A2%0D%0A)%0D%0A−%0D%0A3%0D%0A2%0D%0A(4 points)%0D%0APut responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.%0D%0AWho has more money in their account? Response area%0D%0A%0D%0AWhat is the difference in the amount of money that they have? Response area
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.