Negative Fractional Indices

Rewrite these expressions as a power:
1) 9^-1/2
2) 27^-7/3
I really don't understand this, if you could explain that would be great.
Oh and the last question is:
1/16=2^..?
they want me to find the power but I don't know what I have to do??

The - just means to take the reciprocal.

So to do 9^-1/2, first take 9^1/2, which is the square root of 9 (=3) and flip it over.
The answer for this one is 1/3

For 27^-7/3, take it in steps. First you can take 27 ^(1/3) which is the cube root of 27 ( = 3, again)
Then you can raise 3 to the 7th power 3^7 = 2187, then finally flip it over to account for the -
Answer is 1/2187

For the last one, first figure out that 16 = 2^4. Since the 16 is on the bottom of the fraction, the
power needs to be negative

1/16 = 2^(-4)

Question 1:

9^-1/2 = 1/9^1/2 = 1/sqrt 9 = 1/3

Question 2 :

27^-7/3 = 1/27^7/3 = 1/2187

Last question:

1/16 = 2^-4
It is 2^-4 because 2^-4 = 1/2^4 = 1/16

so therefore you answer is 2^-4

Hope i helped.

1.) .33333333333
2.) . 00045724737

how??? just calculator.

1)
1/3


2)
1/2187