review (1–2 minutes) evaluate each expression for x = 2 and x = -3. 1 ( x^4 ) 2 ( -x^2 + 1 ) 3 ( (-x)^2 - 1 ) 4 ( x^8 ) © carnegie learning, inc.

Question

Accepted Answer

### Problem 1: $ x^4 $
# Explanation:
## Step 1: Evaluate for $ x = 2 $
Substitute $ x = 2 $ into $ x^4 $.
$ 2^4 = 2 \times 2 \times 2 \times 2 = 16 $
## Step 2: Evaluate for $ x = -3 $
Substitute $ x = -3 $ into $ x^4 $.
$ (-3)^4 = (-3) \times (-3) \times (-3) \times (-3) = 81 $
# Answer:
For $ x = 2 $: $ 16 $
For $ x = -3 $: $ 81 $

### Problem 2: $ -x^2 + 1 $
# Explanation:
## Step 1: Evaluate for $ x = 2 $
Substitute $ x = 2 $ into $ -x^2 + 1 $. First, calculate $ x^2 $: $ 2^2 = 4 $. Then, $ -4 + 1 = -3 $
## Step 2: Evaluate for $ x = -3 $
Substitute $ x = -3 $ into $ -x^2 + 1 $. First, calculate $ x^2 $: $ (-3)^2 = 9 $. Then, $ -9 + 1 = -8 $
# Answer:
For $ x = 2 $: $ -3 $
For $ x = -3 $: $ -8 $

### Problem 3: $ (-x)^2 - 1 $
# Explanation:
## Step 1: Evaluate for $ x = 2 $
Substitute $ x = 2 $ into $ (-x)^2 - 1 $. First, calculate $ (-2)^2 = 4 $. Then, $ 4 - 1 = 3 $
## Step 2: Evaluate for $ x = -3 $
Substitute $ x = -3 $ into $ (-x)^2 - 1 $. First, calculate $ (-(-3))^2 = 3^2 = 9 $. Then, $ 9 - 1 = 8 $
# Answer:
For $ x = 2 $: $ 3 $
For $ x = -3 $: $ 8 $

### Problem 4: $ x^8 $
# Explanation:
## Step 1: Evaluate for $ x = 2 $
Substitute $ x = 2 $ into $ x^8 $. $ 2^8 = 256 $ (since $ 2^10 = 1024 $, $ 2^8 = 1024 / 4 = 256 $)
## Step 2: Evaluate for $ x = -3 $
Substitute $ x = -3 $ into $ x^8 $. $ (-3)^8 = 3^8 = 6561 $ (because even exponent makes it positive)
# Answer:
For $ x = 2 $: $ 256 $
For $ x = -3 $: $ 6561 $

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QUESTION IMAGE

Question

Explanation:

Problem 1: \( x^4 \)

Step 1: Evaluate for \( x = 2 \)

Step 2: Evaluate for \( x = -3 \)

Step 1: Evaluate for \( x = 2 \)

Step 2: Evaluate for \( x = -3 \)

Step 1: Evaluate for \( x = 2 \)

Step 2: Evaluate for \( x = -3 \)

Answer:

Problem 2: \( -x^2 + 1 \)