Find the Exact Value (81 1/4)^4

${(81 \frac{1}{4})}^{4}$

Step 1

Convert $81 \frac{1}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

${(81 + \frac{1}{4})}^{4}$

Add $81$ and $\frac{1}{4}$ .

To write $81$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

${(81 \cdot \frac{4}{4} + \frac{1}{4})}^{4}$

Combine $81$ and $\frac{4}{4}$ .

${(\frac{81 \cdot 4}{4} + \frac{1}{4})}^{4}$

Combine the numerators over the common denominator.

${(\frac{81 \cdot 4 + 1}{4})}^{4}$

Simplify the numerator.

Multiply $81$ by $4$ .

${(\frac{324 + 1}{4})}^{4}$

Add $324$ and $1$ .

${(\frac{325}{4})}^{4}$

Step 2

Apply the product rule to $\frac{325}{4}$ .

$\frac{325^{4}}{4^{4}}$

Step 3

Raise $325$ to the power of $4$ .

$\frac{11156640625}{4^{4}}$

Step 4

Raise $4$ to the power of $4$ .

$\frac{11156640625}{256}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{11156640625}{256}$

Decimal Form:

$43580627.4414062$

Mixed Number Form:

$43580627 \frac{113}{256}$