Evaluate each of the following expressions: (-2)^6, (-3)^3, (-10)^5, (-4)^2, (-1)^44

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.

Learn how to evaluate powers of negative numbers, such as (-2)^6 and (-3)^3. Understand the rules for calculating even and odd powers of negative numbers through detailed examples. Suitable for students in Grades 6-8.

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