Evaluate $(a^b)^a - (b^a)^b$ for $a = 2$ and $b = 3$.
We have  \begin{align*}
(a^b)^a - (b^a)^b &= (2^3)^2 - (3^2)^3\\
&=8^2 - 9^3\\
&=64-729\\
&=\boxed{-665}.
\end{align*}
-665
Level 1
Algebra
Problem: Evaluate $(a^b)^a - (b^a)^b$ for $a = 2$ and $b = 3$.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To evaluate the expression $(a^b)^a - (b^a)^b$ for $a = 2$ and $b = 3$, first substitute the values of $a$ and $b$ into the expression. 

Calculate $(2^3)^2$. Start with $2^3$, which equals $8$. Then raise $8$ to the power of $2$: $8^2 = 64$. 

Next, calculate $(3^2)^3$. Start with $3^2$, which equals $9$. Then raise $9$ to the power of $3$: $9^3 = 729$. 

Now, substitute these results back into the expression: $64 - 729$. 

Perform the subtraction: $64 - 729 = -665$. 

Thus, the final answer is $-665$.<|END_OF_LATENT|> The final answer is $-665$.