1. **Stating the problem:** We want to understand what happens if you keep squaring the number 7 repeatedly. 2. **Formula used:** Squaring a number means multiplying it by itself. If we start with a number $a$, then squaring it once gives $a^2$. 3. **Repeated squaring:** If you square the result again, you get $(a^2)^2 = a^{2 \times 2} = a^4$. 4. **General rule:** Each time you square, you raise the original number to the power of $2$ raised to the number of times you have squared it. After $n$ times, the result is: $$7^{2^n}$$ 5. **Example:** - After 1 squaring: $7^2 = 49$ - After 2 squarings: $7^{2^2} = 7^4 = 2401$ - After 3 squarings: $7^{2^3} = 7^8 = 5,764,801$ 6. **Explanation:** The number grows extremely fast because the exponent doubles each time you square the previous result. **Final answer:** Repeatedly squaring 7 results in $7^{2^n}$ after $n$ squarings, which grows very rapidly.