Calculate (2³)⁶: Solving Nested Power Expressions

The power of a power rule says $(a^m)^n = a^{m \cdot n}$. Think of it this way: $(2^3)^6$ means multiply $2^3$ by itself 6 times, creating 18 total factors of 2.

For $2^3 \cdot 2^6$, you add exponents: $2^{3+6} = 2^9$. For $(2^3)^6$, you multiply exponents: $2^{3 \times 6} = 2^{18}$. The parentheses make all the difference!

Yes! You can calculate $2^3 = 8$, then find $8^6$. But using the power rule $(2^3)^6 = 2^{18}$ is much faster and helps you recognize the pattern.

Multiplication of powers: $a^m \cdot a^n = a^{m+n}$ (add exponents)

Power of a power: $(a^m)^n = a^{m \cdot n}$ (multiply exponents)

Look for parentheses - they tell you it's power of a power!

That's the beauty of exponent rules! You don't need to calculate $2^{18}$ (which is 262,144). Just leave your answer as $2^{18}$ - it's the simplest form.