Calculate (2³)⁶: Solving Nested Power Expressions

Question

(23)6= (2^3)^6 =

Step-by-Step Solution

To solve the given expression (23)6 (2^3)^6 , we apply the power of a power rule (am)n=amn (a^m)^n = a^{m \cdot n} . Here, a=2 a = 2 , m=3 m = 3 , and n=6 n = 6 .

Thus, we calculate the exponent:

36=18 3 \cdot 6 = 18

So, (23)6=218 (2^3)^6 = 2^{18} .

Answer

218 2^{18}