If (2^(x^2) × 8^2) / 8^(2x) = 1/8, then the value of 2^(x^2 - 2x + 1) is equal to
A8
B2
C16 ✓ Correct
D4
Correct answer: (C) 16
Explanation
The value of 2^(x^2 - 2x + 1) is 16.
Write 8 = 2^3, so 2^(x^2) * 2^6 / 2^(6x) = 2^(-3).
Equate exponents: x^2 + 6 - 6x = -3.
x^2 - 6x + 9 = 0, so (x - 3)^2 = 0 and x = 3.
2^(x^2 - 2x + 1) = 2^((x - 1)^2) = 2^4 = 16.
Want more like this? Create a free account to practise a full test, track your progress, and get spaced-repetition review.
Practise on Mcqkart →🎓 Book an expert →