Evaluate the two expressions and compare the answers. Do the expressions have the same value? $$ -2^{6} $$ and $$ (-2)^{6} $$ Part: $$ 0 / 3 $$ Part 1 of 3

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Let's evaluate both expressions step by step and compare their values.

### **1. Understanding the Expressions**

- **Expression 1:** $$ -2^{6} $$
- **Expression 2:** $$ (-2)^{6} $$

### **2. Evaluating Each Expression**

#### **Expression 1: $$ -2^{6} $$**

- **Order of Operations:** In mathematics, exponentiation has higher precedence than the unary negative sign. This means you first calculate $$ 2^{6} $$ and then apply the negative sign.
  
  $$
  -2^{6} = -(2^{6}) = -(64) = -64
  $$

- **Result:** $$ -64 $$

#### **Expression 2: $$ (-2)^{6} $$**

- **Order of Operations:** Here, the base of the exponent is $$ -2 $$ because the negative sign is inside the parentheses. You raise the entire base $$ (-2) $$ to the power of 6.
  
  $$
  (-2)^{6} = (-2) \times (-2) \times (-2) \times (-2) \times (-2) \times (-2) = 64
  $$
  
  Alternatively, since the exponent is even, the result will be positive:
  
  $$
  (-2)^{6} = (2)^{6} = 64
  $$

- **Result:** $$ 64 $$

### **3. Comparing the Results**

- **Expression 1:** $$ -64 $$
- **Expression 2:** $$ 64 $$

**Conclusion:** The two expressions do **not** have the same value. $$ -2^{6} = -64 $$ while $$ (-2)^{6} = 64 $$.

This difference arises because, in the first expression, the negative sign is applied *after* raising 2 to the 6th power, resulting in a negative number. In the second expression, the negative base is raised to an even power, which results in a positive number.
$$ -2^{6} = -64 $$ and $$ (-2)^{6} = 64 $$. They do not have the same value.

Evaluate the two expressions and compare the answers. Do the expressions have the same value? \( -2^{6} \) and \( (-2)^{6} \) Part: \( 0 / 3 \) Part 1 of 3

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