Simplify the Radical Expression (81 1/4)^5

${(81 \frac{1}{4})}^{5}$

Step 1

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

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

${(81 + \frac{1}{4})}^{5}$

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

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

${(81 \cdot \frac{4}{4} + \frac{1}{4})}^{5}$

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

${(\frac{81 \cdot 4}{4} + \frac{1}{4})}^{5}$

Combine the numerators over the common denominator.

${(\frac{81 \cdot 4 + 1}{4})}^{5}$

Simplify the numerator.

Multiply $81$ by $4$ .

${(\frac{324 + 1}{4})}^{5}$

Add $324$ and $1$ .

${(\frac{325}{4})}^{5}$

Step 2

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

$\frac{325^{5}}{4^{5}}$

Step 3

Raise $325$ to the power of $5$ .

$\frac{3625908203125}{4^{5}}$

Step 4

Raise $4$ to the power of $5$ .

$\frac{3625908203125}{1024}$