Let's evaluate each of the expressions given:

1. $(-2)^6$:

$(-2)^6 = (-2) \times (-2) \times (-2) \times (-2) \times (-2) \times (-2)$

Calculating step-by-step:

$(-2) \times (-2) = 4$

$4 \times (-2) = -8$

$-8 \times (-2) = 16$

$16 \times (-2) = -32$

$-32 \times (-2) = 64$

So, $(-2)^6 = 64$.

2. $(-3)^3$:

$(-3)^3 = (-3) \times (-3) \times (-3)$

Calculating step-by-step:

$(-3) \times (-3) = 9$

$9 \times (-3) = -27$

So, $(-3)^3 = -27$.

3. $(-10)^5$:

$(-10)^5 = (-10) \times (-10) \times (-10) \times (-10) \times (-10)$

Calculating step-by-step:

$(-10) \times (-10) = 100$

$100 \times (-10) = -1000$

$-1000 \times (-10) = 10000$

$10000 \times (-10) = -100000$

So, $(-10)^5 = -100000$.

4. $(-4)^2$:

$(-4)^2 = (-4) \times (-4)$

$(-4) \times (-4) = 16$

So, $(-4)^2 = 16$.

5. $(-1)^{44}$:

Since the exponent is even, $(-1)$ raised to any even power is $1$.

$(-1)^{44} = 1$

So, $(-1)^{44} = 1$.

In summary, the evaluated expressions are:

1. $(-2)^6 = 64$
2. $(-3)^3 = -27$
3. $(-10)^5 = -100000$
4. $(-4)^2 = 16$
5. $(-1)^{44} = 1$

Would you like further details or have any questions?

Here are some related questions:

1. What happens when you raise a negative number to an odd power?
2. How does raising a number to an even power affect its sign?
3. What is the value of $(-5)^4$?
4. Calculate $(-7)^3$.
5. What is the result of $(-1)^{99}$?

Tip: The sign of a negative number raised to a power depends on whether the exponent is odd or even. If the exponent is odd, the result will be negative; if it's even, the result will be positive.