Use the order of operations to simplify (13 * 2 - 5^2) divided by [3^2 - (-4)]^2.

Step-by-step solution

1. 1

   Treat the fraction bar as a grouping symbol. It acts like invisible brackets around the whole numerator and the whole denominator, so simplify each of them completely before dividing. Nothing may be cancelled across the bar until both sides are single numbers.

2. 2

   Numerator: exponents first, then multiply, then subtract.

   $5^{2}=25,\qquad 13\cdot 2=26,\qquad 26-25=1.$

   The multiplication and the power both outrank the subtraction, so the numerator is $1$.

3. 3

   Denominator: finish the inside of the bracket before squaring. Inside, evaluate the power and then the subtraction of a negative:

   $3^{2}=9,\qquad 9-(-4)=9+4=13.$

   Squaring too early — for instance computing $3^2-(-4)^2=9-16$ — is the classic mistake; the outer exponent belongs to the whole bracket.

4. 4

   Apply the outer exponent.

   $\left[13\right]^{2}=169.$

5. 5

   Divide.

   $\frac{1}{169}.$

   Since $169=13^2$ is not divisible by $1$'s factors beyond $1$, the fraction is already in lowest terms; as a decimal it is $0.005917\ldots$