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.

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.

Answer 1

To evaluate the equation \( 7 - 4 \cdot 7349^{\sqrt{}} = 7 \), we first need to interpret what \( \sqrt{} \) represents. It seems there is some confusion regarding the presence and meaning of \(\sqrt{}\).

Let's simplify this. The equation can be rewritten as:

\[
7 - 4 \cdot 7349^x = 7
\]

If we isolate \( 4 \cdot 7349^x \):

\[
7 - 7 = 4 \cdot 7349^{\sqrt{}} \implies 0 = 4 \cdot 7349^{\sqrt{}}
\]

For this statement to be true, \( 4 \cdot 7349^{\sqrt{}} \) must equal zero. However, since \( 7349^{\sqrt{}} \) is a positive number (assuming \( \sqrt{} \) is a real number), the expression \( 4 \cdot 7349^{\sqrt{}} \) cannot equal zero. Thus, the original equation is false.

Therefore, the correct response is:

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