If 4^(4x) = 1600, then what is the value of (4^(x-1))^2
40
20
10
5/2
5/4
The correct problem is quoted above.
(4^(x-1))^2
= 4^(2x-2)
[Multiply the exponents]
= 4^(2x)/(4^2)
[Exponents subtracted means division]
= 4^(2x)/16
Since 4^(4x) = 1600, 4^(2x) = 40.
[Take the square root of each side]
Thus, 4^(2x)/16 = 40/16 = 5/2.
The correct answer is
D.
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