Simplify the Nested Expression: (a^4)^6 Using Power Rules

Because you're repeating the multiplication! $(a^4)^6$ means $a^4 \times a^4 \times a^4 \times a^4 \times a^4 \times a^4$ - that's 6 groups of 4, which equals 24 total factors of a.

Great question! $a^4 \times a^6 = a^{4+6} = a^{10}$ (you add when multiplying same bases). But $(a^4)^6 = a^{4 \times 6} = a^{24}$ (you multiply when raising a power to a power).

Look for parentheses! If you see $(a^m)^n$ with parentheses, multiply the exponents. If you see $a^m \times a^n$ without parentheses around the first power, add the exponents.

Absolutely! $(a^4)^6$ means $a^4 \times a^4 \times a^4 \times a^4 \times a^4 \times a^4$. Using the rule $a^m \times a^n = a^{m+n}$, you get $a^{4+4+4+4+4+4} = a^{24}$.

Apply the power to everything inside! $(2a^4)^6 = 2^6 \times (a^4)^6 = 64a^{24}$. The coefficient gets raised to the 6th power too.