Arrange the following prefix expressions in ascending order on the basis of…
2025
Arrange the following prefix expressions in ascending order on the basis of their values.
Accessible transcription of the expressions shown in the image:
Expression | Prefix form |
|---|---|
A |
|
B |
|
C |
|
D |
|
Here, · denotes multiplication and ↑ denotes exponentiation. Choose the correct answer from the numbered values below:
A, D, C, B
A, C, D, B
A, B, C, D
C, A, D, B
Answer: B. 2 — CONCEPTIn prefix notation, each operator appears before its operands. Evaluate a binary prefix expression recursively: evaluate the left operand, evaluate the…
- A.
1
- B.
2
- C.
3
- D.
4
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Show answer & explanation
Correct answer: B
CONCEPT
In prefix notation, each operator appears before its operands. Evaluate a binary prefix expression recursively: evaluate the left operand, evaluate the right operand, and then apply the operator in that order. Exponentiation must be completed before its enclosing arithmetic operation.
APPLICATION
For A,
− · 2 / 8 4 3means(2 × (8 ÷ 4)) − 3. Since8 ÷ 4 = 2, the value is(2 × 2) − 3 = 1.For B,
↑ − · 3 6 · 4 2 5means((3 × 6) − (4 × 2))5. The base is18 − 8 = 10, so the value is 105 = 100,000.For C,
+ − ↑ 3 2 ↑ 2 3 / 6 − 4 2means (32 − 23) + (6 ÷ (4 − 2)). This gives (9 − 8) + (6 ÷ 2) = 1 + 3 = 4.For D,
· + 3 + 3 ↑ 3 + 1 1 3means (3 + (3 + 32)) × 3. Since 32 = 9, the value is (3 + 3 + 9) × 3 = 15 × 3 = 45.
CROSS-CHECK
Expression | Value | Ascending rank |
|---|---|---|
A | 1 | 1 |
C | 4 | 2 |
D | 45 | 3 |
B | 100,000 | 4 |
Therefore, the ascending order is A, C, D, B, which is selected by the value 2.