Find the value X ? (2/7)-8 *(7/2)-2 = (2/7)X.
2023
Find the value X ? (2/7)-8 *(7/2)-2 = (2/7)X.
- A.
6
- B.
-6
- C.
4
- D.
-8
Show answer & explanation
Correct answer: B
Concept: To compare or combine two powers, first write them with the SAME base, then apply the law am · an = am+n. A negative exponent means reciprocal: a-1 = 1/a, so a base and its reciprocal are related by an exponent of -1.
Application:
Note that 7/2 is the reciprocal of 2/7, so 7/2 = (2/7)-1.
Therefore (7/2)-2 = ((2/7)-1)-2 = (2/7)(-1)×(-2) = (2/7)2.
Substitute into the given equation: (2/7)-8 × (2/7)2 = (2/7)X.
Apply am · an = am+n on the left side: (2/7)-8+2 = (2/7)-6.
Since the bases on both sides are equal (2/7), the exponents must be equal too: X = -6.
Cross-check: substituting X = -6 back, the right side becomes (2/7)-6, which matches (2/7)-8 × (2/7)2 = (2/7)-8+2 = (2/7)-6, confirming the value.