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The expression to compare is:

\[
\left( \frac{7}{9} \right)^4 \quad \text{or} \quad \left( \frac{9}{7} \right)^4
\]

To determine which is greater, let's evaluate the behavior of both terms:

1. \(\left( \frac{7}{9} \right)^4\) involves a fraction less than 1 raised to a power, which will make the value smaller than 1.
2. \(\left( \frac{9}{7} \right)^4\) involves a fraction greater than 1 raised to a power, which will make the value larger than 1.

Clearly, since \(\left( \frac{9}{7} \right)^4 > 1\) and \(\left( \frac{7}{9} \right)^4 < 1\), the larger expression is \(\left( \frac{9}{7} \right)^4\).

Thus, \(\left( \frac{9}{7} \right)^4\) is greater than \(\left( \frac{7}{9} \right)^4\).

Would you like further details on the reasoning or any questions on the topic?

Here are five related questions:
1. What happens when you raise a fraction less than 1 to a positive power?
2. How do exponents affect the comparison of two fractions?
3. What if the exponent was negative? How would that change the comparison?
4. Can you derive a general rule for comparing powers of two fractions?
5. How do reciprocal relationships affect the comparison of powers?

**Tip:** When comparing powers of fractions, a fraction less than 1 becomes smaller, and a fraction greater than 1 becomes larger when raised to positive powers.

Learn how to compare the exponents of fractions with a detailed solution to determine which is greater between (7/9)^4 and (9/7)^4. Understand the properties of exponents and their effects on fractions. Suitable for Grades 8-10.

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