The expression √((16ˣ + 8ˣ)/(4ˣ + 2ˣ)) simplifies to which of the following?
A) 2
B) 2ˣ
C) 2²ˣ
D) (√2)ˣ
E) √(2ˣ)
IMAT 2023 · Question 55
Q55 - Powers and roots
Pinned
The correct answer is B) 2ˣ.
Write everything in powers of 2 and factor:
16ˣ + 8ˣ = 2³ˣ(2ˣ + 1)
4ˣ + 2ˣ = 2ˣ(2ˣ + 1)
The (2ˣ + 1) cancels and leaves 2²ˣ, and the square root of that is 2ˣ.
Quick check with x = 1: √(24/6) = √4 = 2.
Replies 0
No other replies yet.
Log in to reply.