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

Answer 1

To evaluate the expression \( (-2)^3 \times 3^0 \times (-4)^{-2} \), we can break it down into parts:

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 \( (-4)^{-2} \): \[ (-4)^{-2} = \frac{1}{(-4)^2} \] Now calculate \( (-4)^2 \): \[ (-4)^2 = 16 \] So, \[ (-4)^{-2} = \frac{1}{16} \]

Now we can combine all these results together: \[ (-2)^3 \times 3^0 \times (-4)^{-2} = -8 \times 1 \times \frac{1}{16} \] This simplifies to: \[ -8 \times \frac{1}{16} = -\frac{8}{16} = -\frac{1}{2} \]

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