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When simplifying fractions, one of the key steps involves finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.
For example, in \(\frac{28}{6}\), the GCD of 28 and 6 is 2.::
This means that both 28 and 6 can be divided exactly by 2:
\frac{28}{6} = \frac{28 \div 2}{6 \div 2} = \frac{14}{3}

The process of finding the GCD makes simplification easier and helps reduce fractions to their simplest forms. If you're ever unsure of the GCD, you can use methods like listing out the divisors of each number or using the Euclidean Algorithm.

Multiplying fractions is straightforward if you follow a simple rule: multiply the numerators together and the denominators together. First, take each fraction and lay them out:
\(\frac{14}{3} \cdot \frac{9}{4}\)

Next, multiply the numerators (the top numbers):
14 \cdot 9 = 126
Then, multiply the denominators (the bottom numbers):
3 \cdot 4 = 12

So, the product of the fractions is:
\frac{14}{3} \cdot \frac{9}{4} = \frac{126}{12}
Following these steps will help you easily multiply fractions and simplify your answers. Always remember to simplify the result further, if possible, by finding the greatest common divisor (as discussed in the previous section). In our example, 126 and 12 have a GCD of 6 which makes the final simplified result
\(\frac{126 \div 6}{12 \div 6} = \frac{21}{2}\).

Exponentiation in fractions is another important concept. When a fraction is raised to a power, you simply raise both the numerator and the denominator to that power. Let’s take the fraction \(\frac{3}{2}\) and raise it to the power of 2:
\(\frac{3}{2}\)^2

Both the 3 (numerator) and the 2 (denominator) will be squared:
3^2 = 9
2^2 = 4

Thus, raising \(\frac{3}{2}\) to the power of 2 results in:
\(\frac{3}{2}\)^2 = \frac{9}{4}
This operation can happen with any fraction and any power. Applying these steps consistently will enable you to handle fractions raised to exponents easily. Always ensure to simplify the fractions if possible after performing exponentiation.