I have no idea how to solve this one :D

The two questions are:

 

1) 81 to the power of -2 to the power of -2

2) 81 to the power of (-2) to the power of -2

 

For 1), the expression can be represented numerically as \({81}^{{-2}^{-2}}\)

 

To solve, the first thing that can be done is simplify the -2^-2 above the 81.

 

-2^-2 =

-(2^-2) =

 

When you have a negative power, you do in this example 2^-n, you turn it into 1/2^n:

 

-(2^-2) =

-1/(2^2) =

-1/4

 

Now we have 81^-1/4, which can be solved as follows:

 

81^-1/4 =

\(\sqrt[4]{{81}^{-1}}\) =

\(\sqrt[4]{\frac{1}{81}}\) =

\(\frac{\sqrt[4]{1}}{\sqrt[4]{81}}\) =

\(\frac{1}{3}\)

 

For the second one, it's the same thing, except (-2)^-2:

 

(-2)^-2 =

1/((-2)^2) =

1/4

 

And then 81 ^ 1/4:

 

81^1/4 =

\(\sqrt[4]{{81}^{1}}\) =

3