`((2)/(3)) ^(0) ` = ?

Options

A. `3/2`
B. `2/3`
C. `1`
D. 0

Answer

To solve the expression \(\left(\frac{2}{3}\right)^{0}\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Expression**: We have the expression \(\left(\frac{2}{3}\right)^{0}\).

**Hint**: Recognize that the expression is in the form of a fraction raised to a power.

2. **Apply the Exponent Rule**: According to the exponent rule, any non-zero number raised to the power of zero is equal to 1. This means:
\[ a^{0} = 1 \quad \text{for any } a \neq 0 \]

**Hint**: Remember that this rule applies to any base that is not zero.

3. **Substitute the Base**: Here, our base \(a\) is \(\frac{2}{3}\), which is not zero. Therefore, we can apply the rule:
\[ \left(\frac{2}{3}\right)^{0} = 1 \]

**Hint**: Always check if the base is non-zero before applying the exponent rule.

4. **Final Result**: Thus, the value of \(\left(\frac{2}{3}\right)^{0}\) is:
\[ 1 \]

**Hint**: Conclude by stating the final answer clearly.

### Final Answer:
\[ \left(\frac{2}{3}\right)^{0} = 1 \]