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

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

Step 1

Simplify each term.

Raise $3$ to the power of $2$ .

$9 - {(\frac{1}{4})}^{2}$

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

$9 - \frac{1^{2}}{4^{2}}$

One to any power is one.

$9 - \frac{1}{4^{2}}$

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

$9 - \frac{1}{16}$

Step 2

To write $9$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$9 \cdot \frac{16}{16} - \frac{1}{16}$

Step 3

Combine $9$ and $\frac{16}{16}$ .

$\frac{9 \cdot 16}{16} - \frac{1}{16}$

Step 4

Combine the numerators over the common denominator.

$\frac{9 \cdot 16 - 1}{16}$

Step 5

Simplify the numerator.

Multiply $9$ by $16$ .

$\frac{144 - 1}{16}$

Subtract $1$ from $144$ .

$\frac{143}{16}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{143}{16}$

Decimal Form:

$8.9375$

Mixed Number Form:

$8 \frac{15}{16}$