Simplification of (81x^4/y^-8)^1/4

To simplify the given expression, we need to apply the rules of exponents and simplify the terms inside the brackets.

Step 1: Simplify the numerator

The numerator is 81x^4, which can be written as (3^4)(x^4). Using the rule of exponents, we can simplify this as 3^(4*1/4) x^(4*1/4), which equals 3x.

Step 2: Simplify the denominator

The denominator is y^-8, which can be written as 1/y^8. Using the rule of exponents, we can simplify this as y^(8*-1), which equals 1/y^8.

Step 3: Simplify the expression inside the brackets

Now that we have simplified the numerator and denominator, we can substitute these values into the expression inside the brackets. This gives us:

(3x/1/y^8)^1/4

Using the rule of exponents, we can rewrite this as:

(3x*y^8)^1/4

Step 4: Simplify the expression

Finally, we can simplify the expression by taking the fourth root of 3x*y^8. This gives us:

(3x*y^8)^(1/4) = (3^(1/4)*x^(1/4)*y^2)

Therefore, the simplified value of (81x^4/y^-8)^1/4 is (3^(1/4)*x^(1/4)*y^2).