Question

sama has: $ 5^8 ∙ 5^4/(5^3)^2 in their bank account

jimena has: $ 2^9 ∙ (2^-2)^-3/2 in their bank account

who has more money, and what's the different in the amount of money they have

Answer 1

To compare the amounts of money Sama and Jimena have, we need to simplify the expressions given.

For Sama:
$ 5^8 ∙ 5^4/(5^3)^2

We can simplify this expression using the exponent rules:
First, we can simplify the exponent in the denominator: 5^3 = 125.
Then, we can simplify the expression further:
$ 5^8 ∙ 5^4/125^2

Now, we can simplify the exponents using the rule (a^m)^n = a^(m*n):
$ 5^8 ∙ 5^4/125^2
= $ 5^(8+4)/125^2
= $ 5^12/125^2

For Jimena:
$ 2^9 ∙ (2^-2)^-3/2

We can simplify this expression using the exponent rules:
First, we need to calculate the exponent in the brackets: (2^-2)^-3 = 2^(2*(-3)) = 2^-6.
Then, we can simplify the expression further:
$ 2^9 ∙ 2^-6/2

Now, we can simplify the exponents using the rule a^m/a^n = a^(m-n):
$ 2^9 ∙ 2^-6/2
= $ 2^(9-6)/2
= $ 2^3/2
= $ 8/2
= $ 4

So, Jimena has $ 4 in her bank account, while Sama has $ 5^12/125^2.

To find the difference between the amounts of money they have, we need to subtract:

$ 5^12/125^2 - $ 4

Unfortunately, without knowing the exact values or rounding the expression $ 5^12/125^2, we cannot calculate the exact difference between their amounts of money.