Question 420168
the 4th root of 0 will equal 0.


the basic reversibility property of an equation is:


y = fourth root of x if and only if x = y to the fourth power.


we start with the fourth root of 0 = 0.


this is true if and only if 0 to the fourth power = 0.


0 to the fourth power = 0*0*0*0 which equals 0.


therefore the fourth root of 0 equals 0.


you can verify this is true by using your calculator (assuming your calculator does it correctly which I am assuming is true).


take 0^4 and you will see that your calculator tells you the answer is 0.


take the fourth root of 0 and you will see that your calculator tells you the answer is 0.


to show you how the reversibility property works, we'll take another example where x is not equal to 0.


we start with the fourth root of 16 = 2.


this is true if and only if 2 to the fourth power = 16


take your calculator and find the 4th root of 16.


you will see that the answer is 2.


now take 2 to the 4th power.


you will see that the answer is 16.