simplify: (75x^3 y / 3x^5 y^3) ^3/2

3500 tickets were sold at the carnival. Adult tickers are $35 each and the children's are $20 each. A profit of 10% adult tickets were made and a profit of 5% children tickets. A total profit of $620 was made. Write 2 equations that represent this scenario.

Please help very urgent thanks ALOT !!!

first, I'd simplify the inside:

75x^3y/3x^5y^3 = 15/x^2y^2

Now just multiply exponents by 3/2 and you have

15√15 / x^3y^3

for the tickets,
a+c = 3500
.10(35x) + .05(20y) = 620

Thank you so much, god bless u

To simplify the expression (75x^3y / 3x^5y^3)^(3/2), we can use the rule of exponents that states (a/b)^c = a^c / b^c.

So, applying this rule to our given expression, we have:

(75x^3y / 3x^5y^3)^(3/2) = 75^(3/2) * x^(3/2 - 5(3/2)) * y^(1 - 3(3/2))

Simplifying further, 75^(3/2) = sqrt(75)^3 = 5√(3)^3 = 5 * 3^(3/2) = 5 * 3 * √3 = 15√3

x^(3/2 - 5(3/2)) = x^(3/2 - 15/2) = x^(-12/2) = x^(-6) = 1 / x^6

y^(1 - 3(3/2)) = y^(1 - 9/2) = y^(-7/2) = 1 / y^(7/2) = 1 / √(y^7)

Putting it all together, the simplified expression is:

(75x^3y / 3x^5y^3)^(3/2) = 15√3 * (1 / x^6) * (1 / √(y^7))

For the second part of your question:

Let's say the number of adult tickets sold is "a" and the number of children tickets sold is "c". The profit from selling adult tickets can be calculated as 0.10 * 35 * a, and the profit from selling children tickets can be calculated as 0.05 * 20 * c.

The total profit made is given as $620, so we can write the first equation as:

0.10 * 35 * a + 0.05 * 20 * c = 620

The second equation that represents this scenario is simply the total number of tickets sold multiplied by their respective prices:

35a + 20c = total profit in dollars (which in this case is not specified)

These two equations represent the profit made from selling adult and children tickets at the carnival.