If ` 2^(98) - 2^(97) - 2 ^(96) + 2 ^(95) = m xx 2 ^(95) ` , find the value of m .

Answer

To solve the equation \( 2^{98} - 2^{97} - 2^{96} + 2^{95} = m \cdot 2^{95} \), we will follow these steps:

### Step 1: Factor out the common term
We notice that all terms on the left side of the equation contain powers of 2. The smallest power is \( 2^{95} \). We can factor \( 2^{95} \) out of the left-hand side:

\[ 2^{95}(2^{3} - 2^{2} - 2^{1} + 1) = m \cdot 2^{95} \]

### Step 2: Simplify the expression inside the parentheses
Now we simplify the expression inside the parentheses:

\[ 2^{3} = 8, \quad 2^{2} = 4, \quad 2^{1} = 2 \]

Substituting these values gives:

\[ 2^{3} - 2^{2} - 2^{1} + 1 = 8 - 4 - 2 + 1 \]

### Step 3: Perform the arithmetic
Now we perform the arithmetic step-by-step:

1. \( 8 - 4 = 4 \)
2. \( 4 - 2 = 2 \)
3. \( 2 + 1 = 3 \)

So, we have:

\[ 2^{95} \cdot 3 = m \cdot 2^{95} \]

### Step 4: Divide both sides by \( 2^{95} \)
Since \( 2^{95} \) is common on both sides, we can divide both sides by \( 2^{95} \):

\[ 3 = m \]

### Conclusion
Thus, the value of \( m \) is:

\[ \boxed{3} \]

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