Sure! Let's solve the expression step by step.
We are given the expression:
[tex]\[
\left[3^3 - (-5)^2\right]^5 \div \left\{ \left[(1)^2\right]^2 \right\}^2
\][/tex]
### Step 1: Calculate [tex]\( 3^3 \)[/tex]
[tex]\[
3^3 = 27
\][/tex]
### Step 2: Calculate [tex]\( (-5)^2 \)[/tex]
[tex]\[
(-5)^2 = 25
\][/tex]
### Step 3: Calculate [tex]\( 3^3 - (-5)^2 \)[/tex]
[tex]\[
27 - 25 = 2
\][/tex]
### Step 4: Raise the result of Step 3 to the power of 5
[tex]\[
2^5 = 32
\][/tex]
### Step 5: Calculate [tex]\( (1)^2 \)[/tex]
[tex]\[
(1)^2 = 1
\][/tex]
### Step 6: Raise the result of Step 5 to the power of 2
[tex]\[
1^2 = 1
\][/tex]
### Step 7: Raise the result of Step 6 to the power of 2
[tex]\[
1^2 = 1
\][/tex]
### Step 8: Divide the result of Step 4 by the result of Step 7
[tex]\[
\frac{32}{1} = 32
\][/tex]
So, the final result of the given expression [tex]\(\left[3^3 - (-5)^2\right]^5 \div \left\{ \left[(1)^2\right]^2 \right\}^2\)[/tex] is:
[tex]\[
\boxed{32}
\][/tex]
