The vaue of `(d ^(s + 1)div d * d ^(s))` would be

Options

A. `e ^(2 (s +t))`
B. 1
C. `0`
D. ` d ^( s + t)`

Answer

To solve the expression \((d^{(s + 1)} \div (d \cdot d^{s}))\), we can follow these steps:

### Step 1: Rewrite the expression
The expression can be rewritten as:
\[ \frac{d^{(s + 1)}}{d \cdot d^{s}} \]

### Step 2: Simplify the denominator
In the denominator, we can combine the terms since they have the same base \(d\):
\[ d \cdot d^{s} = d^{1 + s} = d^{(s + 1)} \]

### Step 3: Substitute back into the expression
Now we can substitute this back into our expression:
\[ \frac{d^{(s + 1)}}{d^{(s + 1)}} \]

### Step 4: Apply the properties of exponents
According to the properties of exponents, when we divide two expressions with the same base, we subtract the exponents:
\[ d^{(s + 1) - (s + 1)} = d^{0} \]

### Step 5: Simplify \(d^{0}\)
Any non-zero number raised to the power of 0 is equal to 1:
\[ d^{0} = 1 \]

### Final Answer
Thus, the value of \((d^{(s + 1)} \div (d \cdot d^{s}))\) is:
\[ \boxed{1} \]