For all nanzero real numbers a,b,and c m what is the value of ` a^(0) +b^(0) +c^(0)` ?

Options

A. Undefined
B. `A+b+c`
C. 0
D. 3

Answer

To solve the question, we need to evaluate the expression \( a^0 + b^0 + c^0 \) given that \( a, b, \) and \( c \) are all non-zero real numbers.

**Step-by-step Solution:**

1. **Understanding the Exponent Rule**:
We start by recalling the rule of exponents which states that any non-zero number raised to the power of 0 is equal to 1. Mathematically, this can be expressed as:
\[ x^0 = 1 \quad \text{for any } x \neq 0 \]

2. **Applying the Rule to Each Term**:
Since \( a, b, \) and \( c \) are all non-zero real numbers, we can apply the exponent rule to each term in the expression:
\[ a^0 = 1, \quad b^0 = 1, \quad c^0 = 1 \]

3. **Summing the Results**:
Now we can sum the results of the individual terms:
\[ a^0 + b^0 + c^0 = 1 + 1 + 1 \]

4. **Calculating the Final Result**:
Finally, we perform the addition:
\[ 1 + 1 + 1 = 3 \]

Thus, the value of \( a^0 + b^0 + c^0 \) is \( \boxed{3} \).

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