whats (ab)^4(a^-2/b^-2)^2 equel to

Answer 1

To calculate the given expression, we can simplify each term before raising them to the powers:

(ab)^4 = a^4b^4 (using the property (xy)^n = x^n * y^n)
(a^-2/b^-2)^2 = (1/a^2 * 1/b^-2)^2 (using the property (a/b)^n = a^n/b^n)
= (b^2/a^2)^2 (using the property 1/b^-2 = b^2)
= b^4/a^4

Now, we can substitute these simplified terms back into the original expression:

(a^4b^4)(b^4/a^4) = a^4b^4/b^4a^4 = 1

Therefore, (ab)^4(a^-2/b^-2)^2 is equal to 1.