The expression $-2^6$ can be simplified as follows:

In mathematical order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction), exponents are evaluated before any multiplication or negation. The expression $-2^6$ means that the exponent is applied to $2$ first, and then the result is negated.

$-2^6 = -(2^6) = -(64) = -64$

Therefore, $-2^6 = -64$.

Would you like any further clarification or details?

Here are 5 related questions:

1. What is the value of $(-2)^6$?
2. How do the rules of exponents apply when negative numbers are involved?
3. What is the difference between $-2^6$ and $(-2)^6$?
4. How does the order of operations affect solving expressions like $-3^4$?
5. How would you simplify $3 \times -2^4$?

Tip: Always remember the order of operations (PEMDAS) when simplifying expressions involving exponents.