User
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.
To solve this problem, we need to simplify the expressions for the amount of money both Sama and Jimena have.
Sama: $ 5^8 ∙ 5^4/(5^3)^2
To simplify, we can use the rules of exponents. When multiplying the same base, we add the exponents:
$ 5^8 ∙ 5^4 = 5^(8+4) = 5^12
Now, let's simplify the denominator:
(5^3)^2 = 5^(3*2) = 5^6
So, Sama has $5^12 / 5^6 in their bank account.
Jimena: $ 2^9 ∙ (2^-2)^-3/2
Let's simplify the exponent first:
(2^-2)^-3/2 = 2^(-2*-3/2) = 2^3 = 8
Now, let's substitute the simplified exponent back into the expression:
$ 2^9 ∙ 8/2
Simplifying further:
$ 2^9 ∙ 4
Using the rule of multiplying the same base, we add the exponents:
$ 2^(9+2) = $ 2^11
So, Jimena has $2^11 in their bank account.
To compare the amounts of money they have, we compare the exponents:
$5^12 = (5^2)^6 = 25^6
$2^11 = (2^2)^5 = 4^5
Since $25^6 > $4^5, Sama has more money than Jimena. The difference in the amount of money they have is $25^6 - $4^5.