To analyze the equation \( 7 - 4 \cdot 7^{349} = 7 \), we can simplify it.
First, let's isolate the term involving the exponent:
1. Rearranging the equation gives us:
\[
7 - 7 = 4 \cdot 7^{349}
\]
\[
0 = 4 \cdot 7^{349}
\]
2. The right-hand side, \( 4 \cdot 7^{349} \), is not equal to zero since \( 7^{349} \) is a positive number and multiplying it by anything positive (like 4) will also yield a positive number.
Therefore, the equation \( 7 - 4 \cdot 7^{349} = 7 \) is **false**.
Now let's analyze the provided responses:
1. "False. The answer should be negative since the exponents are negative." - This is incorrect; the exponents being negative does not apply here.
2. "False. When applying the Quotient Property, the final exponent is not 1." - This option is irrelevant to evaluating this case.
3. "True, because the Product Property makes the numerator and the denominator equal." - This does not apply to the equation.
4. "True, because the Quotient Property gives a final exponent of 1." - This does not apply to the equation.
None of the justifications accurately explain the reason for the equation being false.
Thus, the correct answer should be: **False.** The equation does not hold true because \( 4 \cdot 7^{349} \) is not zero.