(9^3/2*5^-2/3/75^-1)^3/4

To simplify the given expression: (9^3/2 * 5^-2/3 / 75^-1)^3/4

First, let's simplify the exponents inside the parentheses: 9^3/2 = (sqrt(9))^3 = 3^3 = 27 5^-2/3 = 1 / (5^(2/3))

Now, let's simplify the denominator of 75^-1: 75^-1 = 1 / 75

Next, let's rewrite the expression with the simplified exponents: (27 * 1 / (5^(2/3)) / (1/75))^3/4

Now, let's simplify the expression inside the parentheses: 27 * 1 / (5^(2/3)) = 27/(5^(2/3)) Since the denominator of 5^(2/3) is a fraction, we need to flip it: 27/(5^(2/3)) = 27 * (5^(3/2))/1

Now, let's simplify the denominator: 1 / 75 = 1/75

Next, we can rewrite the expression as: (27 * (5^(3/2))/1 / (1/75))^3/4

Now, let's simplify the division inside the parentheses: (27 * (5^(3/2))/1) / (1/75) = (27 * (5^(3/2))/1) * (75/1)

Next, let's simplify further: (27 * (5^(3/2))/1) * (75/1) = 27 * (5^(3/2)) * 75

Finally, let's simplify the exponent outside the parentheses: (27 * (5^(3/2)) * 75)^(3/4) = (27 * (5^(3/2)) * 75)^(3/4)

So, the simplified expression is: (27 * (5^(3/2)) * 75)^(3/4)