Evaluate (16^2)/(4^2)+(4^2)/(8^2)

$\frac{16^{2}}{4^{2}} + \frac{4^{2}}{8^{2}}$

Simplify each term.

Raise $16$ to the power of $2$ .

$\frac{256}{4^{2}} + \frac{4^{2}}{8^{2}}$

Raise $4$ to the power of $2$ .

$\frac{256}{16} + \frac{4^{2}}{8^{2}}$

Divide $256$ by $16$ .

$16 + \frac{4^{2}}{8^{2}}$

Raise $4$ to the power of $2$ .

$16 + \frac{16}{8^{2}}$

Raise $8$ to the power of $2$ .

$16 + \frac{16}{64}$

Cancel the common factor of $16$ and $64$ .

Factor $16$ out of $16$ .

$16 + \frac{16 (1)}{64}$

Cancel the common factors.

Factor $16$ out of $64$ .

$16 + \frac{16 \cdot 1}{16 \cdot 4}$

Cancel the common factor.

$16 + \frac{16 \cdot 1}{16 \cdot 4}$

Rewrite the expression.

$16 + \frac{1}{4}$

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

$16 \cdot \frac{4}{4} + \frac{1}{4}$

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

$\frac{16 \cdot 4}{4} + \frac{1}{4}$

Combine the numerators over the common denominator.

$\frac{16 \cdot 4 + 1}{4}$

Simplify the numerator.

Multiply $16$ by $4$ .

$\frac{64 + 1}{4}$

Add $64$ and $1$ .

$\frac{65}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{65}{4}$

Decimal Form:

$16.25$

Mixed Number Form:

$16 \frac{1}{4}$