What is the value of 64 raised to the power of 13?

To calculate 64 raised to the power of 13, we can first express 64 in exponential form. Since 64 is equal to 2 to the power of 6, we have:

64 = 2⁶

Thus, 64¹³ can be rewritten as:

(2⁶)¹³

Using the property of exponents that states (a^m)ⁿ = a^m*n, we can simplify as follows:

64¹³ = 2^6*13 = 2⁷⁸

Now, to find the actual numerical value of 2⁷⁸, we can compute it as:

2⁷⁸ = 288230376151711744

Therefore, the value of 64 raised to the power of 13 is 288230376151711744.