The problem is to evaluate the expression $(-2)^4 \times (-\frac{1}{2})^3$.

ArithmeticExponentsOrder of OperationsInteger ArithmeticFraction Arithmetic
2025/5/25

1. Problem Description

The problem is to evaluate the expression (2)4×(12)3(-2)^4 \times (-\frac{1}{2})^3.

2. Solution Steps

First, evaluate (2)4(-2)^4.
Since the exponent is an even number, the result will be positive.
(2)4=(2)×(2)×(2)×(2)=16(-2)^4 = (-2) \times (-2) \times (-2) \times (-2) = 16
Next, evaluate (12)3(-\frac{1}{2})^3.
Since the exponent is an odd number, the result will be negative.
(12)3=(12)×(12)×(12)=18(-\frac{1}{2})^3 = (-\frac{1}{2}) \times (-\frac{1}{2}) \times (-\frac{1}{2}) = -\frac{1}{8}
Now, multiply the two results.
16×(18)=168=216 \times (-\frac{1}{8}) = -\frac{16}{8} = -2

3. Final Answer

The final answer is -2.

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