Evaluate (-8/17)^2-(15/17)^2

${(- \frac{8}{17})}^{2} - {(\frac{15}{17})}^{2}$

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 $- \frac{8}{17}$ .

${(- 1)}^{2} {(\frac{8}{17})}^{2} - {(\frac{15}{17})}^{2}$

Apply the product rule to $\frac{8}{17}$ .

${(- 1)}^{2} \frac{8^{2}}{17^{2}} - {(\frac{15}{17})}^{2}$

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

$1 \frac{8^{2}}{17^{2}} - {(\frac{15}{17})}^{2}$

Multiply $\frac{8^{2}}{17^{2}}$ by $1$ .

$\frac{8^{2}}{17^{2}} - {(\frac{15}{17})}^{2}$

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

$\frac{64}{17^{2}} - {(\frac{15}{17})}^{2}$

Raise $17$ to the power of $2$ .

$\frac{64}{289} - {(\frac{15}{17})}^{2}$

Apply the product rule to $\frac{15}{17}$ .

$\frac{64}{289} - \frac{15^{2}}{17^{2}}$

Raise $15$ to the power of $2$ .

$\frac{64}{289} - \frac{225}{17^{2}}$

Raise $17$ to the power of $2$ .

$\frac{64}{289} - \frac{225}{289}$

Step 2

Combine fractions.

Combine the numerators over the common denominator.

$\frac{64 - 225}{289}$

Simplify the expression.

Subtract $225$ from $64$ .

$\frac{- 161}{289}$

Move the negative in front of the fraction.

$- \frac{161}{289}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{161}{289}$

Decimal Form:

$- 0.55709342 \dots$