Ask a New Question
Menu

Is the equation 7^−4⋅7^3 devided by √49 =7

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

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.
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.

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

1 answer

To evaluate the expression \( 7^{-4} \cdot 7^3 \div \sqrt{49} \), let's break it down step by step.

  1. Calculate \( \sqrt{49} \): \[ \sqrt{49} = 7 \]

  2. Rewrite the expression: The expression now looks like: \[ 7^{-4} \cdot 7^3 \div 7 \]

  3. Apply the Product Property: We can combine the terms in the numerator: \[ 7^{-4} \cdot 7^3 = 7^{-4 + 3} = 7^{-1} \]

  4. Rewrite the division: The expression turns into: \[ \frac{7^{-1}}{7} = 7^{-1 - 1} = 7^{-2} \]

  5. Evaluate \( 7^{-2} \): \[ 7^{-2} = \frac{1}{7^2} = \frac{1}{49} \]

Now let's compare this result with \( 7 \). Clearly, \( \frac{1}{49} \) is not equal to \( 7 \).

Therefore, the statement is:

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