## College Algebra (6th Edition)

$\frac{1}{121}$
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.