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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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The value of M in (qp)2M+2=(pq)9−M is:
2−7
11
6
5
11
Invert the base on one side by changing the sign of its exponent, then equate the exponents directly since the bases are equal.
The given equation is (p/q)2M+2=(q/p)9−M
(ba)x=(ab)−x
Invert the base on one side by changing the sign of its exponent, then equate the exponents directly since the bases are equal.
Forgetting to change the sign of the exponent when taking the reciprocal of the base.
Step 1: Write the given equation
We are given the equation involving powers of fractions: (p/q)2M+2=(q/p)9−M
(qp)2M+2=(pq)9−M
Step 2: Express both sides with the same base
Since pq=(qp)−1, we can rewrite the right side with base qp: (q/p)9−M=(p/q)−(9−M)
(p/q)2M+2=(p/q)−9+M
Step 3: Equate the exponents
Since the bases on both sides are equal, their exponents must be equal: 2M+2=−9+M
2M+2=M−9
Step 4: Solve for M
Subtract M from both sides and subtract 2 from both sides: 2M−M=−9−2⇒M=−11
M=−11
B is correct because solving the equation 2M+2=−(9−M) yields M=−11.
Similar exponent comparison techniques are frequently used in algebraic equations and exponential growth/decay problems.
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