Solve for \( x \) \( \frac{7^{7}}{7^{3}}=7^{x} \) \( x=\square \)

To solve for \( x \), we can simplify the left side of the equation using the properties of exponents. Specifically, we can apply the quotient rule, which states that \[ \frac{a^m}{a^n} = a^{m-n} \] Using this rule: \[ \frac{7^{7}}{7^{3}} = 7^{7-3} = 7^{4} \] This means that we can rewrite the equation as: \[ 7^{4} = 7^{x} \] Since the bases are the same, we can set the exponents equal to each other: \[ 4 = x \] Thus, the solution is \( x = 4 \).