13.5 * x^(19/4) * y^(38/12)
this can be simplified to:
13.5 * x^(19/4) * y^(19/6)
see my worksheet for the steps that i took to get to the simplified anaswer.
i verified with random values of x and y that the original expression and the final expression give you the answer.
here's my worksheet.
step 1 translates the numerator to exponential form and simplifies it using the following conecpts.
square root of (x) = x^(1/2)
(a * x^b * y^c) ^ d = a^d * (x^b)^d * (y^c)^d = a^d * x^(b*d) * y^(c*d)
step 2 translates the denominator to exponential form and simplifies it using the following concepts.
fourth root of (x) = x^(1/4)
(a * x^b * y^c) ^ d = a^d * (x^b)^d * (y^c)^d = a^d * x^(b*d) * y^(c*d)
step 3 translates x^a / x^b to x^(a-b) and y^c / y^d to y(c-d)
the fractional exponents are then simnplified as much as possible.
the basic rules for exponent arithmetic are:
x^a * x^b = x^(a + b)
x^a / x^b = x^(a - b)
(x^a)^b = x^(a * b)
x^(-a) = 1/x^a)
(x^a / y^b) ^ c = (x^a)^c / (y^b)^c = x^(a*c) / y^(b*c)
(x^a * y^b) ^ c = (x^a)^c * (y^b)^c = x^(a*c) * y^(b*c)
here's a reference on exponent arithmetic.
https://www.mathplanet.com/education/pre-algebra/discover-fractions-and-factors/powers-and-exponents
here's another.
https://www.mathplanet.com/education/pre-algebra/discover-fractions-and-factors/powers-and-exponents
this reference has 5 pages associated with it for a complete tutorial.