Solve (-16)^1/4
since 16 = 2^4, this is
2i^(1/4) = sqrt(2)(1+i)
I do not get it.....
To solve (-16)^(1/4), we need to apply the rules of exponents.
First, let's break it down step by step:
Step 1: Simplify the exponent.
Since the exponent is 1/4, it is asking for the fourth root of -16.
Step 2: Find the fourth root of -16.
To calculate the fourth root of a number, we need to find a number that, when multiplied by itself four times, equals -16.
Let's break it down further:
(-16)^(1/4) = (16 * -1)^(1/4) = 16^(1/4) * (-1)^(1/4)
Now, we just need to find the fourth root of 16 and simplify -1 to the power of 1/4.
Step 3: Find the fourth root of 16.
The fourth root of 16 is 2 because 2 * 2 * 2 * 2 = 16.
Step 4: Simplify -1 to the power of 1/4.
When a negative number is raised to an exponent involving an even denominator, it results in an imaginary number. Therefore, (-1)^(1/4) = √(-1) = i, where i represents the imaginary unit.
Step 5: Combine the results.
Putting it all together, we have:
(-16)^(1/4) = 16^(1/4) * (-1)^(1/4) = 2 * i = 2i
So, the solution to (-16)^(1/4) is 2i.