To solve the equation \( w \cdot (16 \cdot 56) = (88 \cdot 16) \cdot 56 \), we can use the properties of multiplication, specifically the associative property which allows us to regroup numbers.
First, we can simplify both sides of the equation.
On the right side: \[ (88 \cdot 16) \cdot 56 \] We can calculate \( 88 \cdot 16 \) first: \[ 88 \cdot 16 = 1408 \] Now substitute back: \[ (88 \cdot 16) \cdot 56 = 1408 \cdot 56 \] Now we can compute \( 1408 \cdot 56 \): \[ 1408 \cdot 56 = 78944 \]
Now we equate both sides: \[ w \cdot (16 \cdot 56) = 78944 \]
Next, we simplify \( 16 \cdot 56 \): \[ 16 \cdot 56 = 896 \]
Now substitute in: \[ w \cdot 896 = 78944 \]
To find \( w \), we can divide both sides by 896: \[ w = \frac{78944}{896} \]
Calculating \( \frac{78944}{896} \): \[ w = 88 \]
Hence, the value of \( w \) that makes the multiplication sentence true is: \[ \boxed{88} \]