By algebraic handling, the expression 9 / 6 - 4 · (2 / 3 - 7 / 6)² is equivalent to the expression 1 / 2.
In this problem we must simplify an expressions involving powers and rational numbers by algebra definitions and theorems:
9 / 6 - 4 · (2 / 3 - 7 / 6)² Given
9 / 6 - 4 · [[(2 · 6) - (3 · 7)] / (3 · 6)]² Subtraction of fractions with different denominators
9 / 6 - 4 · [(12 - 21) / 18]² Definition of multiplication
9 / 6 - 4 · (- 9 / 18)² Definition of subtraction
3 / 2 - 4 · (1 / 2)² Definition of simplification
3 / 2 - 4 · (1 / 4) Power properties
3 / 2 - 1 Definition of division / Existence of multiplicative inverse
3 / 2 - 2 / 2 Definition of division / Existence of multiplicative inverse
1 / 2 Subtraction of fractions with same denominator / Result
To learn more on rational numbers: https://brainly.com/question/17450097
#SPJ1
