Simplify the Radical Expression (16 1/4)^3

${(16 \frac{1}{4})}^{3}$

Convert $16 \frac{1}{4}$ to an improper fraction.

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

${(16 + \frac{1}{4})}^{3}$

Add $16$ and $\frac{1}{4}$ .

To write $16$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

${(16 \cdot \frac{4}{4} + \frac{1}{4})}^{3}$

Combine $16$ and $\frac{4}{4}$ .

${(\frac{16 \cdot 4}{4} + \frac{1}{4})}^{3}$

Combine the numerators over the common denominator.

${(\frac{16 \cdot 4 + 1}{4})}^{3}$

Simplify the numerator.

Multiply $16$ by $4$ .

${(\frac{64 + 1}{4})}^{3}$

Add $64$ and $1$ .

${(\frac{65}{4})}^{3}$

Apply the product rule to $\frac{65}{4}$ .

$\frac{65^{3}}{4^{3}}$

Raise $65$ to the power of $3$ .

$\frac{274625}{4^{3}}$

Raise $4$ to the power of $3$ .

$\frac{274625}{64}$