Question

Simplify the expression 12^5 / 12^3 using the Quotient Rule of Exponents. Provide the step-by-step solution.

Answer 1

To simplify the expression \( \frac{12^5}{12^3} \) using the Quotient Rule of Exponents, we will follow these steps:

1. **Identify the Quotient Rule**: The Quotient Rule states that for any non-zero number \( a \) and integers \( m \) and \( n \):
\[
\frac{a^m}{a^n} = a^{m-n}
\]

2. **Apply the Quotient Rule**: In our case, we have:
- \( a = 12 \)
- \( m = 5 \)
- \( n = 3 \)

Using the Quotient Rule:
\[
\frac{12^5}{12^3} = 12^{5-3}
\]

3. **Perform the subtraction in the exponent**:
\[
5 - 3 = 2
\]

So, we have:
\[
12^{5-3} = 12^2
\]

4. **Calculate \( 12^2 \)**:
\[
12^2 = 12 \times 12 = 144
\]

5. **Conclusion**: The simplified form of \( \frac{12^5}{12^3} \) is:
\[
\boxed{144}
\]