Say true or false and justify your answer:
`3^(0)=(1000)^0`

Answer

To determine whether the statement \(3^{0} = (1000)^{0}\) is true or false, we can follow these steps:

### Step 1: Understand the property of exponents
According to the properties of exponents, any non-zero number raised to the power of zero is equal to 1. This means that:
\[ a^{0} = 1 \quad \text{for any } a \neq 0 \]

### Step 2: Apply the property to \(3^{0}\)
Using the property from Step 1:
\[ 3^{0} = 1 \]

### Step 3: Apply the property to \((1000)^{0}\)
Similarly, applying the same property to \(1000\):
\[ (1000)^{0} = 1 \]

### Step 4: Compare the two results
Now we can compare the results from Step 2 and Step 3:
\[ 3^{0} = 1 \quad \text{and} \quad (1000)^{0} = 1 \]
Thus, we have:
\[ 3^{0} = (1000)^{0} \]

### Step 5: Conclusion
Since both sides of the equation are equal (both are 1), we can conclude that the statement \(3^{0} = (1000)^{0}\) is **true**.

### Justification
The justification for our conclusion is based on the exponent rule that states any non-zero number raised to the power of zero equals 1.

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