Simplify 1/2+(3/8-1/8)^2

$\frac{1}{2} + {(\frac{3}{8} - \frac{1}{8})}^{2}$

Simplify each term.

Combine the numerators over the common denominator.

$\frac{1}{2} + {(\frac{3 - 1}{8})}^{2}$

Subtract $1$ from $3$ .

$\frac{1}{2} + {(\frac{2}{8})}^{2}$

Cancel the common factor of $2$ and $8$ .

Factor $2$ out of $2$ .

$\frac{1}{2} + {(\frac{2 (1)}{8})}^{2}$

Cancel the common factors.

Factor $2$ out of $8$ .

$\frac{1}{2} + {(\frac{2 \cdot 1}{2 \cdot 4})}^{2}$

Cancel the common factor.

$\frac{1}{2} + {(\frac{2 \cdot 1}{2 \cdot 4})}^{2}$

Rewrite the expression.

$\frac{1}{2} + {(\frac{1}{4})}^{2}$

Apply the product rule to $\frac{1}{4}$ .

$\frac{1}{2} + \frac{1^{2}}{4^{2}}$

One to any power is one.

$\frac{1}{2} + \frac{1}{4^{2}}$

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

$\frac{1}{2} + \frac{1}{16}$

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{1}{2} \cdot \frac{8}{8} + \frac{1}{16}$

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{8}{8}$ .

$\frac{8}{2 \cdot 8} + \frac{1}{16}$

Multiply $2$ by $8$ .

$\frac{8}{16} + \frac{1}{16}$

Combine the numerators over the common denominator.

$\frac{8 + 1}{16}$

Add $8$ and $1$ .

$\frac{9}{16}$

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{16}$

Decimal Form:

$0.5625$