Questions: b. (-2)^4 d. (-2)^5 ÷ (-2) f. (-1)^151 h. 9 - 4 * 7 - 2(-5) + 4 j. -2^10 + 2^10

Transcript text: b. $(-2)^{4}$ d. $(-2)^{5} \div(-2)$ f. $(-1)^{151}$ h. $9-4 \cdot 7-2(-5)+4$ j. $-2^{10}+2^{10}$

Solution

Solution Steps

Solution Approach

b. Calculate the power of -2 raised to 4. d. Calculate the power of -2 raised to 5 and then divide by -2. f. Calculate the power of -1 raised to 151. h. Evaluate the arithmetic expression involving subtraction, multiplication, and addition. j. Calculate the power of -2 raised to 10, add it to the power of 2 raised to 10.

Step 1: Calculate $ (-2)^4 $

To find $ (-2)^4 $: \[ (-2)^4 = 16 \]

Step 2: Calculate $ \frac{(-2)^5}{-2} $

To find $ \frac{(-2)^5}{-2} $: \[ (-2)^5 = -32 \quad \text{and thus} \quad \frac{-32}{-2} = 16.0 \]

Step 3: Calculate $ (-1)^{151} $

To find $ (-1)^{151} $: \[ (-1)^{151} = -1 \]

Step 4: Evaluate $ 9 - 4 \cdot 7 - 2(-5) + 4 $

To evaluate the expression: \[ 9 - 4 \cdot 7 - 2(-5) + 4 = 9 - 28 + 10 + 4 = -5 \]

Step 5: Calculate $ -2^{10} + 2^{10} $

To find $ -2^{10} + 2^{10} $: \[ -2^{10} = -1024 \quad \text{and} \quad 2^{10} = 1024 \quad \text{thus} \quad -1024 + 1024 = 0 \]

Final Answer

\[ \text{b. } 16, \quad \text{d. } 16.0, \quad \text{f. } -1, \quad \text{h. } -5, \quad \text{j. } 0 \] \[ \boxed{16, \, 16.0, \, -1, \, -5, \, 0} \]

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