Simplify $\frac{{\left(5^2\right)}^3\times 5^{-4}}{5^3}$ and give the answer as a power of 5.

Power of a power first: ${\left(5^2\right)}^3=5^{2\times 3}=5^6$. The numerator becomes $5^6\times 5^{-4}=5^2$, and dividing gives $5^{2-3}=5^{-1}$. Adding instead of multiplying in step one gives $5^5$ and leads to the trap $5^{-2}$.