Simplify 1/3(1-1/4)^2

$\frac{1}{3} {(1 - \frac{1}{4})}^{2}$

Step 1

Simplify the expression.

Write $1$ as a fraction with a common denominator.

$\frac{1}{3} \cdot {(\frac{4}{4} - \frac{1}{4})}^{2}$

Combine the numerators over the common denominator.

$\frac{1}{3} \cdot {(\frac{4 - 1}{4})}^{2}$

Subtract $1$ from $4$ .

$\frac{1}{3} \cdot {(\frac{3}{4})}^{2}$

Apply the product rule to $\frac{3}{4}$ .

$\frac{1}{3} \cdot \frac{3^{2}}{4^{2}}$

Step 2

Combine.

$\frac{1 \cdot 3^{2}}{3 \cdot 4^{2}}$

Step 3

Cancel the common factor of $3^{2}$ and $3$ .

Factor $3$ out of $1 \cdot 3^{2}$ .

$\frac{3 (1 \cdot 3)}{3 \cdot 4^{2}}$

Cancel the common factors.

Factor $3$ out of $3 \cdot 4^{2}$ .

$\frac{3 (1 \cdot 3)}{3 (4^{2})}$

Cancel the common factor.

$\frac{3 (1 \cdot 3)}{3 \cdot 4^{2}}$

Rewrite the expression.

$\frac{1 \cdot 3}{4^{2}}$

Step 4

Simplify the expression.

Multiply $3$ by $1$ .

$\frac{3}{4^{2}}$

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

$\frac{3}{16}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{16}$

Decimal Form:

$0.1875$