Question

Is the equation 7−4⋅7349√=7 true or false? Select the response that correctly answers the question and provides the appropriate justification.(1 point) Responses False. The answer should be negative since the exponents are negative. False. The answer should be negative since the exponents are negative. False. When applying the Quotient Property, the final exponent is not 1. False. When applying the Quotient Property, the final exponent is not 1. True, because the Product Property makes the numerator and the denominator equal. True, because the Product Property makes the numerator and the denominator equal. True, because the Quotient Property gives a final exponent of 1. True, because the Quotient Property gives a final exponent of 1.

Answer 1

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.