Solve ((3^9)^4x)^5y: Multi-Variable Nested Exponent Problem

The power rule says $(a^m)^n = a^{m \cdot n}$. When you raise a power to another power, you're multiplying the base by itself exponentially more times, so the exponents multiply!

Treat variables like regular numbers when multiplying exponents. So 4x × 5y = 20xy, just like 4 × 5 = 20, but with variables included.

Work from the inside out, like peeling layers of an onion. Start with the innermost parentheses and apply the power rule step by step until all parentheses are removed.

Break it down: $3^9$ raised to $4x$ gives $3^{9 \cdot 4x} = 3^{36x}$, then raised to $5y$ gives $3^{36x \cdot 5y} = 3^{180xy}$.

Addition rule is for $a^m \cdot a^n = a^{m+n}$ (same bases multiplied). Power rule is for $(a^m)^n = a^{m \cdot n}$ (powers raised to powers). Make sure you're using the right one!