Question

What is the value of this expression: (-2)^3 x 3^0 x (-4)^-2

Answer 1

To solve the expression \((-2)^3 \times 3^0 \times (-4)^{-2}\), we will evaluate each part step by step:

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

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

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

Now, we can substitute these values back into the original expression:
\[
(-2)^3 \times 3^0 \times (-4)^{-2} = -8 \times 1 \times \frac{1}{16}
\]

Next, simplify the multiplication:
\[
-8 \times 1 = -8
\]
Then,
\[
-8 \times \frac{1}{16} = -\frac{8}{16} = -\frac{1}{2}
\]

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