two students have bank accounts
sama: $ 5^8*5^4/(5^3)^2
jimea: $ 2^9*(2^-2)_3 / 2
who has more money in here acc?
what is the diffrence in the amount of money that they have?
To compare the amount of money in their accounts, we can evaluate the given expressions:
Sama: $5^8 * 5^4 / (5^3)^2
First, simplify the exponents:
$5^(8+4) / 5^(3*2)
$5^12 / 5^6
Now, apply the rule of dividing exponents with the same base (subtract the exponents):
$5^(12-6)
$5^6
This means Sama has $5^6 in her account.
Jimea: $2^9 * (2^(-2))_3 / 2
Evaluating the exponent in base 2, (-2) in the subscript 3 means 2^(-2) = 1/2^2 = 1/4.
Now, calculate the expression:
$2^9 * (1/4) / 2
Dividing by 2 is the same as multiplying by 1/2:
$2^9 * (1/4) * (1/2)
= $2^9 * 1/8
Now, simplify the exponents:
= $2^(9-3)
= $2^6
This means Jimea has $2^6 in her account.
Comparing the amounts:
$5^6 vs. $2^6
Both have the same exponent, so we compare the bases.
5 is greater than 2, therefore Sama has more money in her account.
To find the difference in the amount of money they have, we subtract the smaller amount from the larger amount:
$5^6 - $2^6
= $15625 - $64
= $15561
So, Sama has $15,561 more in her account than Jimea.
does sama have 7 times as much as jimea
No, Sama does not have 7 times as much as Jimea. We can compare their amounts:
Sama: $5^6
Jimea: $2^6
To find out if Sama has 7 times as much money as Jimea, we can divide Sama's amount by Jimea's amount:
$5^6 / $2^6
Using the rule of dividing exponents with the same base (subtract the exponents):
$5^(6-6) / 2^(6-6)
$5^0 / 2^0
Any number (except zero) raised to the power of 0 is equal to 1. Therefore, the expression simplifies to:
1 / 1
Which means Sama does not have 7 times as much money as Jimea.