https://file.aiquickdraw.com/mathbot/file/17267085107065pt5guaf.jpg

The expression in the image is:

\[
\frac{4^{14}}{4^{12}}
\]

To simplify this, we use the properties of exponents. Specifically, the quotient rule of exponents states that:

\[
\frac{a^m}{a^n} = a^{m-n}
\]

Here, \(a = 4\), \(m = 14\), and \(n = 12\). Applying the rule:

\[
\frac{4^{14}}{4^{12}} = 4^{14-12} = 4^2
\]

Now, we calculate \(4^2\):

\[
4^2 = 16
\]

Thus, the simplified result of the given expression is **16**.

Would you like further details or have any questions about this solution?

Here are five related questions to explore further:

1. What is the general rule for multiplying powers with the same base?
2. How would you simplify \(\frac{5^{10}}{5^3}\)?
3. What is the value of \(3^4 \times 3^2\)?
4. Can you express \(16\) as a power of \(2\)?
5. How do exponent rules change when dealing with negative exponents?

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

Learn how to simplify the expression 4^14 / 4^12 using the quotient rule of exponents. This problem demonstrates key concepts in exponents and simplifies to 4^2, which equals 16. Suitable for students in Grades 7-9.

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