(81x^4/y^-8)^1/4 has simplified value equal to?

Question

Answer

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

Step 1: Rewrite the expression

Using the rule that (a/b)^n = a^n/b^n, we can rewrite the expression as:

(81x^4/y^-8)^1/4 = (81x^4)^1/4 / (y^-8)^1/4

Step 2: Simplify the numerator

Using the rule that (a^m)^n = a^mn, we can simplify the numerator as:

(81x^4)^1/4 = 81^(1/4) * (x^4)^1/4 = 3x

Step 3: Simplify the denominator

Using the rule that (a^-n) = 1/a^n, we can simplify the denominator as:

(y^-8)^1/4 = y^-2

Step 4: Combine the simplified numerator and denominator

Substituting the simplified numerator and denominator back into the original expression, we get:

(81x^4/y^-8)^1/4 = (3x) / y^-2 = 3xy^2

Final Answer:

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