Let's solve the given expression step by step: [tex]\( (-2)^2 \cdot (-2)^3 \cdot (-2)^{-4} \)[/tex].
1. Step 1: Calculate [tex]\( (-2)^2 \)[/tex]
[tex]\[ (-2)^2 = (-2) \times (-2) = 4 \][/tex]
2. Step 2: Calculate [tex]\( (-2)^3 \)[/tex]
[tex]\[ (-2)^3 = (-2) \times (-2) \times (-2) = -8 \][/tex]
3. Step 3: Calculate [tex]\( (-2)^{-4} \)[/tex]
[tex]\[ (-2)^{-4} = \frac{1}{(-2)^4} = \frac{1}{16} = 0.0625 \][/tex]
4. Step 4: Multiply the results of the above steps
[tex]\[ 4 \cdot (-8) \cdot 0.0625 \][/tex]
5. Step 5: Multiply the first two terms
[tex]\[ 4 \cdot (-8) = -32 \][/tex]
6. Step 6: Multiply the result by the third term
[tex]\[ -32 \cdot 0.0625 = -2 \][/tex]
So, the answer to the expression [tex]\( (-2)^2 \cdot (-2)^3 \cdot (-2)^{-4} \)[/tex] is:
[tex]\[ \boxed{-2} \][/tex]
