Is the equation 7−4⋅7349√=7

Question

true or false? Select the response that correctly answers the question and provides the appropriate justification.(1 point)
Responses

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

Answer 1

To determine if the equation \( 7 - 4 \cdot 7349^{\sqrt{}} = 7 \) is true or false, we need to analyze the left-hand side of the equation:

1. Evaluate \( 4 \cdot 7349^{\sqrt{}} \): Without knowing the specific value of \(\sqrt{}\) (which isn't defined here), we can't compute this term directly. However, since \( 7349^{\sqrt{}} \) will produce a positive value (because any positive number raised to any power is positive), multiplying it by \( 4 \) will also yield a positive value.

2. Subtract from 7: This means that \( 7 - 4 \cdot 7349^{\sqrt{}} \) will result in something less than \( 7 \) if \( 4 \cdot 7349^{\sqrt{}} \) is positive.

Thus, the equation simplifies to:

\[ 7 - \text{positive number} \neq 7 \]

Consequently, the equation \( 7 - 4 \cdot 7349^{\sqrt{}} = 7 \) does not hold true.

Given the provided options, the correct response is:

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

(Note: This statement seems a bit misleading as it references the Quotient Property. The reasoning mainly revolves around the understanding that subtracting a positive number from \(7\) cannot yield \(7\)).