Final answer:
The expression (((x^(4)y)/(y^(4)))^((6)/(5)) can be simplified to (x^(12/5))/(y^(12/5)). The values of r and t, the exponents of x and y, respectively, are both 12/5.
Step-by-step explanation:
The expression ((x^(4)y)/(y^(4)))^((6)/(5)) can be simplified by using the property of exponents that states ((a^b)^c) = a^(b*c). Therefore, we can rewrite the expression as (x^(4*(6/5)))/(y^(4*(6/5))). Simplifying further, we get (x^(24/5))/(y^(24/5))
To simplify the expression, we can convert the fractional exponents to radical form. 24/5 can be written as √(x^24) / √(y^24). Using the property that √(a^b) = (a^(b/2)), we can simplify the expression to x^(24/10) / y^(24/10). Lastly, we can simplify the fractions as x^(12/5) / y^(12/5).
Therefore, the value of r, the exponent of x, is 12/5 and the value of t, the exponent of y, is also 12/5.