Write each power as radical
1. 12^1/4
2. (-50)^5/3
we've done a bunch of these -- how about you take a stab at these first?
I'm don't get it man My brain is fried
12^(1/4) = ∜12
(-50)^(5/3) = ∛(-50)^5
just remember that the nth root is the 1/n power
since
∛x * ∛x * ∛x = ∛x^3 = x,
expressed as powers, you need
x^(1/3) * x^(1/3) * x^(1/3)
= x^(1/3 + 1/3 + 1/3)
= x^1
= x
To write each power as a radical, we can follow a simple rule: the exponent in the power becomes the index of the radical and the number inside the radical remains the same. Let's apply this rule to the given powers:
1. 12^(1/4):
To write this power as a radical, we will use the fourth root since the exponent in the power is 1/4. The number inside the radical will remain 12.
So, 12^(1/4) can be written as ∛∛∛∛12.
2. (-50)^(5/3):
To write this power as a radical, we will use the cubed root since the exponent in the power is 5/3. The number inside the radical will remain -50.
Since we cannot take the cubed root of a negative number, we need to take the absolute value of -50 first (which is 50).
So, (-50)^(5/3) can be written as ∛∛∛50.
Remember that when taking the root of a number, the answer can be positive or negative.