Question

What is the value of this expression: (−2)^3×3^0×(−4)−^2
(1 point)
Responses

1/2
1 half

3/4
3 fourths

−1/2
negative 1 half

0
0

-2

Answer 1

To evaluate the expression \((-2)^3 \times 3^0 \times (-4)^{-2}\), we can break it down step by step.

1. **Calculate \((-2)^3**:
\[
(-2)^3 = -2 \times -2 \times -2 = -8
\]

2. **Calculate \(3^0**:
Any non-zero number raised to the power of 0 is 1:
\[
3^0 = 1
\]

3. **Calculate \((-4)^{-2}**:
The negative exponent means we take the reciprocal:
\[
(-4)^{-2} = \frac{1}{(-4)^2}
\]
Now calculate \((-4)^2\):
\[
(-4)^2 = 16
\]
Thus,
\[
(-4)^{-2} = \frac{1}{16}
\]

4. **Now combine all parts**:
\[
(-2)^3 \times 3^0 \times (-4)^{-2} = -8 \times 1 \times \frac{1}{16}
\]
This simplifies to:
\[
-8 \times \frac{1}{16} = \frac{-8}{16} = -\frac{1}{2}
\]

Putting it all together, the value of the expression is:
\[
\boxed{-\frac{1}{2}}
\]