Two students have bank accounts:

Question

Sama: $ (5 ^ 8 * 5 ^ 4)/((5 ^ 3) ^ 2)

Jimena: \$ (2 ^ n * (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?

Sama

::

They both have the same amount of money

#0 difference in the accounts

#Jimena

7 times more money

$1000

#$523

$759

Answer 1

To solve this problem, we need to simplify the expressions for Sama and Jimena's bank accounts.

For Sama:
Sama: $ (5 ^ 8 * 5 ^ 4)/((5 ^ 3) ^ 2)

Using the rule of exponents (a^m * a^n = a^(m+n), and (a^m)^n = a^(m*n)), we can simplify this expression as follows:

Sama: $ 5^(8+4)/(5^(3*2))

Sama: $ 5^12/5^6

Using the rule of exponents (a^m/a^n = a^(m-n)), we can simplify this expression further:

Sama: $ 5^(12-6)

Sama: $ 5^6

Now let's simplify Jimena's expression:

Jimena: $ (2 ^ n * (2 ^ - 2) ^ - 3)/2

Using the rule of exponents (a^m * a^n = a^(m+n) and (a^m)^n = a^(m*n)), we can simplify this expression as follows:

Jimena: $ (2^n * 2^(-2*-3))/2

Jimena: $ (2^n * 2^6)/2

Using the rule of exponents (a^m/a^n = a^(m-n)), we can simplify this expression further:

Jimena: $ 2^(n+6)/2

Jimena: $ 2^(n+6-1)

Jimena: $ 2^(n+5)

Since we don't have a specific value for n, we can't determine the exact amounts of money in their bank accounts. However, we can make some general observations based on the simplified expressions.

Comparing the simplified expressions, we see that Sama has $5^6 in her account, while Jimena has $2^(n+5) in her account.

If n is any positive number, then Jimena's account will have more money than Sama's account because 2^(n+5) will always be greater than 5^6. Therefore, Jimena has more money in her account.

The exact difference in the amount of money they have can't be determined without knowing the value of n.