3 to the power of 4 divided by 12 to the power of 2

Let's solve the expression \( \frac{3^4}{12^2} \):

1. First, calculate \( 3^4 \):
   \[
   3^4 = 3 \times 3 \times 3 \times 3 = 81
   \]

2. Next, calculate \( 12^2 \):
   \[
   12^2 = 12 \times 12 = 144
   \]

3. Now, divide the two results:
   \[
   \frac{3^4}{12^2} = \frac{81}{144}
   \]

4. Simplify the fraction:
   \[
   \frac{81}{144} = \frac{9}{16}
   \]

Thus, the final result is \( \frac{9}{16} \).

Would you like any further details or explanation on this solution? Here are 5 questions to explore:

1. What is the general formula for dividing powers with the same base?
2. How do you simplify a fraction in general?
3. How would the result change if the bases were different?
4. Can you apply prime factorization to simplify the original expression?
5. What happens if both exponents increase by 1?

**Tip:** When simplifying fractions, always check for the greatest common divisor (GCD) of the numerator and denominator to reduce the fraction effectively.

Learn how to simplify the expression 3^4 divided by 12^2. This step-by-step guide walks through exponentiation and fraction simplification techniques. Suitable for students in Grades 6-8.

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