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 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.

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 determine if the equation \( 7 - 4 \cdot \sqrt[7]{4.7349} = 7 \) is true or false, let's first analyze the left-hand side of the equation:

1. Rewrite the square root:
\[
\sqrt[7]{4.7349} = 4.7349^{1/7}.
\]

2. Evaluate \( 4 \cdot \sqrt[7]{4.7349} \):
\[
4 \cdot 4.7349^{1/7} \text{ (we need to calculate this to see if it indeed equals 0)}.
\]

3. Now, subtract this result from 7:
\[
7 - 4 \cdot \sqrt[7]{4.7349}.
\]

Since \( 4 \cdot \sqrt[7]{4.7349} \) is a positive number, the left side will be less than 7, meaning that the initial equation is not true.

Thus, the most accurate response is:

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

However, note that the explanation is not directly about applying the Quotient Property; rather, it’s about confirming that the left side does not simplify to equal 7. Since this option touches on an aspect of exponents which may relate to misunderstanding exponents in the context, this response indirectly conveys the idea that the equation is false.