# Nzjzmzmizksnd

## Tuana_Uyduran said @sorumatikbot

To evaluate the given mathematical expression, let’s simplify it step by step:

[
\left[ \left( -\frac{1}{2} \right)^3 \cdot (-2^4) \div (-2)^2 \right]^{-1}
]

### Step 1: Simplify the Inner Terms

1. Evaluate (\left( -\frac{1}{2} \right)^3):
[
\left( -\frac{1}{2} \right)^3 = -\frac{1}{2} \cdot -\frac{1}{2} \cdot -\frac{1}{2} = -\frac{1}{8}
]

2. Evaluate ((-2)^4):
[
(-2)^4 = (-2) \cdot (-2) \cdot (-2) \cdot (-2) = 16
]

3. Evaluate (((-2)^2)):
[
(-2)^2 = 4
]

### Step 2: Substitute Back in the Expression

Now substituting these values back into the main expression:
[
\left[ \left( -\frac{1}{8} \right) \cdot 16 \div 4 \right]^{-1}
]

### Step 3: Simplify Inside the Brackets

1. Evaluate (\left( -\frac{1}{8} \cdot 16 \right)):
[
-\frac{1}{8} \cdot 16 = -2
]

2. Now, simplify the division:
[
-2 \div 4 = -\frac{1}{2}
]

So the expression inside the brackets simplifies to:
[
\left[ -\frac{1}{2} \right]^{-1}
]

### Step 4: Apply the Inverse Exponent

To find the inverse:
[
\left( -\frac{1}{2} \right)^{-1} = -2
]

Therefore, the simplified value of the given expression is:

[
\boxed{-2}
]

Türkçe çözer misin

## Tuana_Uyduran said @sorumatikbot: Türkçe çözer misin

[
\left[ \left( -\frac{1}{2} \right)^3 \cdot (-2^4) \div (-2)^2 \right]^{-1}
]

1. (\left( -\frac{1}{2} \right)^3) ifadesini hesaplayalım:
[
\left( -\frac{1}{2} \right)^3 = -\frac{1}{2} \cdot -\frac{1}{2} \cdot -\frac{1}{2} = -\frac{1}{8}
]

[
(-2)^4 = (-2) \cdot (-2) \cdot (-2) \cdot (-2) = 16
]

[
(-2)^2 = 4
]

Bu değerleri ana ifadeye tekrar yerine koyalım:
[
\left[ \left( -\frac{1}{8} \right) \cdot 16 \div 4 \right]^{-1}
]

1. (\left( -\frac{1}{8} \cdot 16 \right)) ifadesini hesaplayalım:
[
-\frac{1}{8} \cdot 16 = -2
]

[
-2 \div 4 = -\frac{1}{2}
]

[
\left[ -\frac{1}{2} \right]^{-1}
]

### Adım 4: Ters Üssel İşlemi Uygulama

Tersini almak için:
[
\left( -\frac{1}{2} \right)^{-1} = -2
]

[
\boxed{-2}
]