Solve Triple Nested Exponents: ((y^6)^8)^9 Simplification Challenge

When you raise a power to a power, you're creating repeated multiplication. For example, $(y^6)^8$ means $y^6 \times y^6 \times y^6...$ (8 times), so you multiply: 6 × 8 = 48.

Work from the inside out! First simplify $(y^6)^8 = y^{48}$, then raise that result to the 9th power: $(y^{48})^9 = y^{432}$.

Yes! Since you're multiplying exponents at each step, you can multiply all three: 6 × 8 × 9 = 432. This gives the same answer as working step by step.

Remember: same base, add exponents when multiplying (like $x^2 \times x^3 = x^5$), but multiply exponents when raising a power to a power (like $(x^2)^3 = x^6$).

Think about it logically: you're multiplying the base y by itself 432 times total. You can verify by multiplying the exponents: 6 × 8 × 9 = 432 ✓