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?
To compare the amounts of money in their accounts, let's simplify the expressions:
Sama: $ 5^8⋅5^4/(5^3)^2 = $ 5^(8+4)/(5^6) = $ 5^12/(5^6) = $ 5^(12-6) = $ 5^6
Jimena: $ 2^9⋅(2^−2)^−3/2 = $ 2^(9-2*(-3))/2 = $ 2^(9+6)/2 = $ 2^15/2 = $ 2^(15-1) = $ 2^14
Therefore, Sama has more money in her account than Jimena.
The difference in the amount of money they have is:
$ 5^6 - $ 2^14