Final answer:
To show that (16^((1)/(4)))^(3) and (16^(3))^((1)/(4)) are equivalent, we can simplify each expression separately and then compare the results.
Step-by-step explanation:
To show that (16^((1)/(4)))^(3) and (16^(3))^((1)/(4)) are equivalent, we can simplify each expression separately and then compare the results.
Let's start with (16^((1)/(4)))^(3). Using the exponent rules, we can multiply the exponents to get ((16^((1)/(4)))^(3)) = 16^(((1)/(4)) x 3) = 16^((3)/(4)).
Now, let's simplify (16^(3))^((1)/(4)). Using the exponent rules again, we can multiply the exponents to get (16^(3))^((1)/(4)) = 16^((3 x (1)/(4))) = 16^((3)/(4)).
Since (16^((1)/(4)))^(3) and (16^(3))^((1)/(4)) simplify to the same expression, we can conclude that they are equivalent.