Answer
$\frac{1}{121}$
Work Step by Step
Use the order of operations to simplify the expression:$$\frac{5\times2-3^{2}}{[3^{2}-(-2)]^{2}}$$
As fraction itself defines grouping symbols, the numerator and denominator are each individual groups. Within each group start with grouping symbols, then move to exponents:$$=\frac{5\times2-9}{[9-(-2)]^{2}}$$
Next complete all multiplication and division in the order it appears left to right within each group:$$=\frac{10-9}{[9+2]^{2}}$$
Finally complete all addition and subtraction in the order it appears left to right in each group$$=\frac{1}{[11]^{2}}$$
As the group within the denominator is fully simplified, we can now complete the exponent:$$=\frac{1}{121}$$This is the final solution as it can not be simplifed.
