Simplify the root.
The square root of (-x)^14.
Why is the answer the absolute value x^7?
To simplify the square root of (-x)^14, we need to understand the properties of exponents and the definition of absolute value.
First, let's break it down step by step:
1. Start with (-x)^14.
- This expression means we have the negative of x raised to the power of 14.
- For simplicity, let's call (-x) as "a."
- So, our expression becomes a^14.
2. Now, let's find the square root of a^14.
- The square root of any number raised to an even power can be simplified to the absolute value of the number raised to half of the power.
- In our case, we have the square root of a^14, so the square root of "a" raised to 14 divided by 2.
- Therefore, we have |a^7|.
3. Let's substitute "a" back into the expression.
- We originally defined "a" as (-x), so we substitute it back: |(-x)^7|.
Finally, the absolute value simplifies the negative sign and gives us the positive value. Therefore, the square root of (-x)^14 simplifies to |(-x)^7|, which can also be written as |x^7|.