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)

Question

Responses

True, because the Quotient Property gives a final exponent of 1.
True, because the Quotient Property gives a final exponent of 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.

False. When applying the Quotient Property, the final exponent is not 1.
False. When applying the Quotient Property, the final exponent is not 1.

False. The answer should be negative since the exponents are negative.
False. The answer should be negative since the exponents are negative.

Answer 1

To evaluate whether the equation \(7 - 4 \cdot 7^{349} = 7\) is true or false, let's simplify the left side:

1. Start with the equation: \[ 7 - 4 \cdot 7^{349} \]

2. Factor out 7 from the expression: \[ 7(1 - 4 \cdot 7^{348}) \]

Now, we have: \[ 7(1 - 4 \cdot 7^{348}) \]

3. Since \(7^{348}\) is a very large number, \(4 \cdot 7^{348}\) is also a very large number, making \(1 - 4 \cdot 7^{348}\) negative.

So, overall, the expression \(7(1 - 4 \cdot 7^{348})\) must be negative and cannot equal \(7\).

Thus, the statement is False.

The most appropriate justification among the options provided is:

• False. When applying the Quotient Property, the final exponent is not 1.

However, this justification does not directly relate to the problem presented. While the final conclusion is correct, the explanation about the Quotient Property does not apply here, as there was no use of the Quotient Property in the expression worked through. The focus should be on the overall simplification and the behavior of the numbers involved.