To determine whether the equation \((7^{-4} \cdot 7^{3}) / (\sqrt{49}) = 7\) is true or false, we can simplify both sides of the equation step by step.
First, simplify the numerator:
\[
7^{-4} \cdot 7^{3}
\]
Using the Product Property of exponents, which states that \(a^m \cdot a^n = a^{m+n}\):
\[
7^{-4 + 3} = 7^{-1}
\]
Next, simplify the denominator:
\[
\sqrt{49} = 7
\]
Now we have:
\[
\frac{7^{-1}}{7}
\]
Using the Quotient Property of exponents, which states that \(\frac{a^m}{a^n} = a^{m - n}\):
\[
\frac{7^{-1}}{7^1} = 7^{-1 - 1} = 7^{-2}
\]
Now, we want to know if:
\[
7^{-2} = 7
\]
This is false because \(7^{-2} = \frac{1}{7^2} = \frac{1}{49}\), which does not equal \(7\).
Therefore, the correct response is:
**False. When applying the Quotient Property, the final exponent is not 1.**