How much is 64 to the power of 13?

The value of 64 to the power of 13, or 64¹³, is an extremely large number. To understand how we arrive at this, we first note that 64 can be expressed as 2 to the power of 6 (since 2⁶ = 64). Therefore, we can rewrite the expression as:

64¹³ = (2⁶)¹³

Using the laws of exponents, we multiply the exponents:

(2⁶)¹³ = 2^{6 * 13} = 2⁷⁸

Calculating 2⁷⁸ directly gives us the value of 64¹³ which equals:

2⁷⁸ = 302,285,172,866,210,000

So, the answer is 302,285,172,866,210,000.