The value of `(d^(s+t)-:d^(s))-:d^(t)` would be

Options

A. a) `d^(2(5+1))`
B. b) `1`
C. c) `0`
D. d) `d^(s-1)`

Answer

To solve the expression \((d^{s+t} \div d^s) \div d^t\), we will follow the laws of exponents step by step.

### Step-by-step Solution:

1. **Rewrite the Expression**:
Start with the original expression:
\[ \frac{d^{s+t}}{d^s} \div d^t \]

2. **Apply the Division Law of Exponents**:
According to the law of exponents, \(\frac{a^m}{a^n} = a^{m-n}\). We can apply this to the first part of the expression:
\[ \frac{d^{s+t}}{d^s} = d^{(s+t) - s} = d^{t} \]
Now, the expression becomes:
\[ d^t \div d^t \]

3. **Apply the Division Law Again**:
Now, apply the division law again to the new expression:
\[ \frac{d^t}{d^t} = d^{t-t} = d^0 \]

4. **Evaluate \(d^0\)**:
By the property of exponents, any non-zero number raised to the power of 0 is equal to 1:
\[ d^0 = 1 \]

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