The value of `((2^(a))^(b c))/((5^(b))^( a c))`, where a = 2, b = 3, and c = 0, is

Options

A. `-1`
B. `(2)/(5)`
C. 1
D. 0

Answer

To solve the expression \(\frac{(2^a)^{bc}}{(5^b)^{ac}}\) where \(a = 2\), \(b = 3\), and \(c = 0\), we can follow these steps:

### Step-by-Step Solution:

1. **Substitute the values of a, b, and c into the expression:**
\[ \frac{(2^2)^{3 \cdot 0}}{(5^3)^{2 \cdot 0}} \]

2. **Calculate the products in the exponents:**
\[ 3 \cdot 0 = 0 \quad \text{and} \quad 2 \cdot 0 = 0 \]
Therefore, the expression simplifies to:
\[ \frac{(2^2)^{0}}{(5^3)^{0}} \]

3. **Evaluate the powers:**
Any non-zero number raised to the power of 0 is equal to 1:
\[ (2^2)^{0} = 1 \quad \text{and} \quad (5^3)^{0} = 1 \]
So now we have:
\[ \frac{1}{1} \]

4. **Final simplification:**
\[ \frac{1}{1} = 1 \]

Thus, the value of the expression is \(1\).