Solve: (2²)³ + (3³)⁴ + (9²)⁶ - Nested Exponents Challenge

The power rule $(a^m)^n = a^{m \times n}$ comes from repeated multiplication. When you have $(2^2)^3$, you're multiplying $2^2$ by itself 3 times, which means multiplying the exponents!

$(2^2)^3 = 2^6 = 64$ but $2^2 \times 2^3 = 2^5 = 32$. The parentheses matter! Nested exponents use the power rule, while separate terms use the product rule.

Apply the power rule: $(9^2)^6 = 9^{2 \times 6} = 9^{12}$. Even though 9 isn't a prime number, the same rule applies to any base!

The question asks for the expression in exponential form, so $2^6 + 3^{12} + 9^{12}$ is the correct final answer. Don't calculate the actual numbers unless specifically asked!

Think of it as repeated multiplication. $(2^2)^3$ means "$2^2$ multiplied by itself 3 times", so you get $2^2 \times 2^2 \times 2^2 = 2^{2+2+2} = 2^6$.