<s>[INST] What is wrong with this problem We know that:
$(a^n)^m=a^{nm}$
From this we have:
$-3^3=[(-3)^2]^\frac{3}{2}=(3^2)^\frac{3}{2}=27$
Find what's wrong
 [/INST] The "law of exponents" that you cite:
$$\large (a^n)^m=a^{nm}$$ 
applies PROVIDED $\bf{a \gt 0}$. 
Here, though, we have $\,\bf{a = -3 \lt 0}$, and hence:
$$-3^3=[(-3)^2]^{\large\frac{3}{2}}=(3^2)^{\large\frac{3}{2}}=27\quad \Longleftarrow \;\text{ False}.$$
$$-3^3 = -(3^3) = -[(3^2)^{\large \frac{3}{2}}] = -(9^{\large \frac{3}{2}}) = -27\quad \Longleftarrow \; \text{ True}$$
But why the trouble? It is a very straightforward computation: 
$$-3^3 = -(3^3) = -(3\cdot 3\cdot 3) = -27$$
</s>