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: $$\boxed{{\displaystyle -\frac{1}{2}}}$$