Final answer:
The calculated value of 3²/4 - 2³/4 is 1/4 after evaluating the exponents and simplifying the expression. This result does not match any of the provided answer options.
Step-by-step explanation:
The question asks to calculate the value of 3²/4 - 2³/4. When solving mathematical expressions involving exponents and division, it's essential to correctly apply the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).
Firstly, calculate the exponents: 3², which is 3 multiplied by itself (3 x 3), equals 9. And 2³, which is 2 multiplied by itself three times (2 x 2 x 2), equals 8. So the expression now reads 9/4 - 8/4.
Next, we divide each term by 4: 9/4 is 2.25, and 8/4 is 2. The expression simplifies to 2.25 - 2 = 0.25, which can be represented as a fraction 1/4. This is not one of the originally provided options (A) 1/2, (B) 5/4, (C) 7/4, (D) 3/2, leading to the conclusion that the question may be misinterpreted or the available options are erroneous.