Is the equation 7−4⋅7349√=7 true or false? Select the response that correctly answers the question and provides the appropriate justification.

Question

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

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

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

True, because the Product Property makes the numerator and the denominator equal.

Answer 1

The equation \( 7 - 4 \cdot 7^{\frac{349}{\sqrt{7}}} = 7 \) can be analyzed step by step.

First, let's simplify the left side:

1. Rewrite the equation: \[ 7 - 4 \cdot 7^{\frac{349}{\sqrt{7}}} = 7 \]

2. For this equation to hold, we can isolate the term involving the exponent: \[ -4 \cdot 7^{\frac{349}{\sqrt{7}}} = 0 \]

3. This would imply that \( 7^{\frac{349}{\sqrt{7}}} \) must equal 0. However, \( 7^{\frac{349}{\sqrt{7}}} \) is never zero, as any exponentiation of a positive number is also positive.

Given this analysis, the equation is indeed false.

So, the correct response is:

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