## Calculating (81 1/4)^4: A Step-by-Step Guide

This article explores the calculation of (81 1/4)^4. This might seem daunting at first glance, but we can break it down into manageable steps.

### Converting to a Fraction

First, we need to convert the mixed number 81 1/4 to an improper fraction.

- Multiply the whole number (81) by the denominator of the fraction (4): 81 * 4 = 324
- Add the numerator of the fraction (1): 324 + 1 = 325
- Keep the same denominator: 325/4

Now our problem becomes (325/4)^4.

### Applying the Exponent

To raise a fraction to a power, we raise both the numerator and the denominator to that power:

(325/4)^4 = (325^4) / (4^4)

### Calculating the Numerator and Denominator

We can use a calculator to find 325^4 = 1,093,789,062,500 and 4^4 = 256.

### Final Result

Therefore, (81 1/4)^4 = (325/4)^4 = **(1,093,789,062,500) / 256**. This can also be expressed as a mixed number or a decimal if needed.

### Key Takeaways

- Converting mixed numbers to improper fractions makes calculations easier.
- Raising a fraction to a power means raising both numerator and denominator to that power.
- Calculators can be helpful for large numbers, but understanding the process is crucial.