Evaluate (-5/13)^2-(12/13)^2

${(- \frac{5}{13})}^{2} - {(\frac{12}{13})}^{2}$

Step 1

Simplify each term.

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{5}{13}$ .

${(- 1)}^{2} {(\frac{5}{13})}^{2} - {(\frac{12}{13})}^{2}$

Apply the product rule to $\frac{5}{13}$ .

${(- 1)}^{2} \frac{5^{2}}{13^{2}} - {(\frac{12}{13})}^{2}$

Raise $- 1$ to the power of $2$ .

$1 \frac{5^{2}}{13^{2}} - {(\frac{12}{13})}^{2}$

Multiply $\frac{5^{2}}{13^{2}}$ by $1$ .

$\frac{5^{2}}{13^{2}} - {(\frac{12}{13})}^{2}$

Raise $5$ to the power of $2$ .

$\frac{25}{13^{2}} - {(\frac{12}{13})}^{2}$

Raise $13$ to the power of $2$ .

$\frac{25}{169} - {(\frac{12}{13})}^{2}$

Apply the product rule to $\frac{12}{13}$ .

$\frac{25}{169} - \frac{12^{2}}{13^{2}}$

Raise $12$ to the power of $2$ .

$\frac{25}{169} - \frac{144}{13^{2}}$

Raise $13$ to the power of $2$ .

$\frac{25}{169} - \frac{144}{169}$

Step 2

Combine fractions.

Combine the numerators over the common denominator.

$\frac{25 - 144}{169}$

Simplify the expression.

Subtract $144$ from $25$ .

$\frac{- 119}{169}$

Move the negative in front of the fraction.

$- \frac{119}{169}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{119}{169}$

Decimal Form:

$- 0.70414201 \dots$