Two students have bank accounts:
Sama: $ (5 ^ 8 * 5 ^ 4)/((5 ^ 3) ^ 2)
Jimena: \$ (2 ^ 9 * (2 ^ - 2) ^ - 3)/2
What is the difference in the amount of money that they have?
7 times more money
$1000
$523
$759
To simplify Sama's expression, we can use the property of exponents that states that when you have a power to a power, you multiply the exponents:
$ (5^8 * 5^4) / ((5^3)^2) = 5^(8+4) / 5^(3*2) = 5^12 / 5^6 = 5^(12-6) = 5^6.
To simplify Jimena's expression, we can use the property of exponents that states that when you have a negative exponent, you can move it to the denominator:
$ (2^9 * (2^-2)^-3) / 2 = 2^9 * 2^6 / 2 = 2^(9+6) / 2 = 2^15 / 2 = 2^(15-1) = 2^14.
So, Sama has $5^6 and Jimena has $2^14.
To find the difference in the amount of money they have, we subtract Jimena's amount from Sama's amount:
$5^6 - $2^14 ≈ $759.
Therefore, the difference in the amount of money that they have is $759.