If (3/4)−6 × (4/3)−8 = (3/4)n, then the value of n is
2023
If (3/4)−6 × (4/3)−8 = (3/4)n, then the value of n is
Answer: E. None of the above — ConceptFor any nonzero base a, a negative exponent means taking the reciprocal: a−m = (1/a)m. When powers have the same base, multiplying them adds their…
- A.
1
- B.
4
- C.
3
- D.
More than one of the above
- E.
None of the above
Attempted by 7 students.
Show answer & explanation
Correct answer: E
Concept
For any nonzero base a, a negative exponent means taking the reciprocal: a−m = (1/a)m.
When powers have the same base, multiplying them adds their exponents: ap × aq = ap+q.
Application
Rewrite the reciprocal-base term: (4/3)−8 = (3/4)8.
Now the bases match: (3/4)−6 × (3/4)8 = (3/4)−6+8.
Add the exponents: −6 + 8 = 2, so n = 2.
Cross-check
Substituting n = 2 gives (3/4)2. The left side also becomes (3/4)−6+8 = (3/4)2, so both sides agree.
Therefore, n = 2; because 2 is not one of the listed numerical choices, the applicable choice is “None of the above”.