Question

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

3/4
3 fourths

−1/2
negative 1 half

1/2
1 half

0
0

-2
-2

Answer 1

Let's evaluate the expression step-by-step:

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

2. Evaluate \( 3^0 \):
\[
3^0 = 1
\]

3. Evaluate \( (-4)^{-2} \):
\[
(-4)^{-2} = \frac{1}{(-4)^2} = \frac{1}{16}
\]

Now, combine these values:
\[
(-2)^3 \times 3^0 \times (-4)^{-2} = -8 \times 1 \times \frac{1}{16}
\]

4. Now compute \( -8 \times \frac{1}{16} \):
\[
-8 \times \frac{1}{16} = -\frac{8}{16} = -\frac{1}{2}
\]

Thus, the value of the expression is:
\[
-\frac{1}{2}
\]

The correct response is **−1/2** (negative 1 half).