If `5^(-k) = 1/t`, then the value of `5^(3k)` is equal to :

Options

A. `1/(3t)`
B. 3t
C. `t^3`
D. data insufficient

Answer

To solve the equation \( 5^{-k} = \frac{1}{t} \) and find the value of \( 5^{3k} \), we can follow these steps:

### Step 1: Rewrite the given equation
We start with the equation:
\[ 5^{-k} = \frac{1}{t} \]
Using the property of exponents that states \( a^{-x} = \frac{1}{a^x} \), we can rewrite the left side:
\[ \frac{1}{5^k} = \frac{1}{t} \]

### Step 2: Cross-multiply to find a relationship
Cross-multiplying gives us:
\[ t = 5^k \]

### Step 3: Find \( 5^{3k} \)
Now, we need to find \( 5^{3k} \). We can express \( 5^{3k} \) in terms of \( t \):
\[ 5^{3k} = (5^k)^3 \]
Substituting \( 5^k = t \) from Step 2:
\[ 5^{3k} = t^3 \]

### Conclusion
Thus, the value of \( 5^{3k} \) is:
\[ \boxed{t^3} \]