Simplify (4^x)^y: Solving Double Exponent Expressions

When you raise a power to another power, you're essentially multiplying the base by itself multiple times. For example, $(4^2)^3$ means $4^2 \cdot 4^2 \cdot 4^2$, which equals $4^{2+2+2} = 4^6$.

Add exponents when multiplying same bases: $4^x \cdot 4^y = 4^{x+y}$. Multiply exponents when raising a power to a power: $(4^x)^y = 4^{xy}$.

The rule works the same way! For example, $(4^{-2})^3 = 4^{(-2) \cdot 3} = 4^{-6}$ or $(4^{1/2})^4 = 4^{(1/2) \cdot 4} = 4^2$.

Look for parentheses! If you see $(something)^{power}$, you multiply exponents. If you see $base^{power} \cdot base^{power}$, you add exponents.

Yes! Try $x = 2, y = 3$: $(4^2)^3 = 16^3 = 4096$ and $4^{2 \cdot 3} = 4^6 = 4096$. They match! ✓