((256m^5)/(n))^1/8((625n^-1)/(m^4))^1/4= square (Simplify your answer.Type exponential notation with p

Question

Answer 1

To simplify the given expression, we need to apply the properties of exponents and simplify each part separately.Given expression:

First, let's simplify \(\left(\frac{256m^5}{n}\right)^{1/8}\):

We know that

, so:

Thus,

Next, let's simplify \(\left(\frac{625n^{-1}}{m^4}\right)^{1/4}\):

We know that

, so:

And,

Thus,

Now, we combine the two simplified parts:

Multiply the numerators and denominators:

Simplify the exponents:

Since

and

, we get:

Thus, the simplified form of the given expression is:

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