To solve for \( x \) in the equation

\[
\frac{7^7}{7^3} = 7^x
\]

we can use the properties of exponents. Specifically, the rule \(\frac{a^m}{a^n} = a^{m-n}\) applies here.

1. Rewrite the left side using the property:

   \[
   \frac{7^7}{7^3} = 7^{7 - 3}
   \]

2. Simplify the exponent:

   \[
   7^{7 - 3} = 7^4
   \]

3. Now we have:

   \[
   7^x = 7^4
   \]

Since the bases are the same, the exponents must be equal. Therefore,

\[
x = 4
\]

### Answer:
\[
x = 4
\]

Would you like more details or have any questions?

Here are 5 related questions to practice similar concepts:

1. Solve for \( x \) in \( \frac{5^8}{5^2} = 5^x \).
2. If \( 2^x = \frac{2^{10}}{2^4} \), what is \( x \)?
3. Simplify \( \frac{9^5}{9^3} \) and express the answer as \( 9^y \).
4. Find \( x \) in the equation \( \frac{a^9}{a^x} = a^3 \).
5. Determine \( x \) if \( \frac{10^{15}}{10^x} = 10^5 \).

**Tip:** When dividing powers with the same base, subtract the exponents.

Learn how to solve the exponential equation \dfrac{7^{7}}{7^3}=7^x using properties of exponents. This problem demonstrates how to apply the rule \frac{a^m}{a^n} = a^{m-n} to simplify expressions. Ideal for Grades 7-8 students studying exponents and algebra.

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