SOLUTION: Can someone please help me solve these??? 1.(-16)^1/4 2. 25^-3/2 3. (-27x^9)1/3

Question 257399: Can someone please help me solve these???
1.(-16)^1/4
2. 25^-3/2
3. (-27x^9)1/3
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
When working with fractional exponents you need to know about the properties of exponents:

Let's see how these properties help us simplify your expressions:
1.
By property #6

This expression represents the 4th root of -16. In other words the number which, when raised to the 4th power, results in -16. There are no such numbers in the set of Real numbers. Whenever we raise a Real number to the 4th power we always get a positive result. If you have never heard of Complex Numbers then we can go no further so skip to #2.

If you know about Complex Numbers, Complex Numbers in Polar form and finding roots of Complex Numbers then we can come up with an answer. Writing as a Complex Number in Polar form we get:

Using deMoivre's (spelling?) Theorem this is equal to:

Which simplifies as follows:

This is the primary 4th root. The other 3 are:

2.
By property #5 above this is equal to:

By property #6 the denominator can be written as or . Since the second form looks easier (after all we do know what the square root of 25 is) we will use that form:

3.
Using property #4 above we get:

Using property #6 on the first part and property #3 on the second part we get:

which simplifies to:

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