Rewrite with positive exponents. Assume that even roots are of nonnegative quantities and that all denominators are nonzero. (2x/y2)^-4

(a/b)^-c= (b/a)^c

To rewrite the expression (2x/y^2)^-4 with positive exponents, we can apply the rule of negative exponents. The rule states that any base raised to a negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent.

In this case, we have (2x/y^2)^-4. To eliminate the negative exponent, we can rewrite it as 1/(2x/y^2)^4.

Next, let's rewrite the expression inside the parentheses raised to the positive exponent. To do this, we apply the rule of exponents for division. The rule states that when dividing two expressions with the same base, we can subtract the exponents.

So, we have 1/(2^4 * (x/y^2)^4).

Now, let's simplify further. The exponent of 2 is 4, and the exponent of (x/y^2) is 4. Applying the rule of exponents, we can simplify (x/y^2)^4 as (x^4)/(y^2)^4.

Now, we have 1/(2^4 * (x^4)/(y^2)^4).

Simplifying the expression inside the parentheses, we get 1/(16 * (x^4)/(y^8)).

To divide by a fraction, we can multiply by its reciprocal. Let's rewrite 1/(16 * (x^4)/(y^8)) as 1 * (y^8)/(16 * x^4).

Finally, we have (y^8)/(16 * x^4) as the expression with positive exponents.