[16x^5y^10/81xy^2)^3/4
To simplify the expression (16x^5y^10/81xy^2)^3/4, follow these steps:
Step 1: Simplify the numerator and denominator inside the parentheses:
16/81 = 2/9
x^5/x = x^(5-1) = x^4
y^10/y^2 = y^(10-2) = y^8
So the expression becomes (2/9x^4y^8)^3/4.
Step 2: Apply the exponent to each term:
(2/9)^3/4 = Cube root of 2/9, then take the fourth root of the result.
x^4^3/4 = x^3
y^8^3/4 = y^6
Putting it all together, the simplified expression is: (∛(2/9)*x^3*y^6).