If (25^{1 – x} times 5^{x + 2} div (frac{1}{125})^{x} = 625^{-1}), find the value of x.
-
A.
x = -4 -
B.
x = 2 -
C.
x = -2 -
D.
x = 4
Correct Answer: Option A
Explanation
(25^{1 – x} times 5^{x + 2} div (frac{1}{125})^{x} = 625^{-1})
((5^2)^{(1 – x)} times 5^{(x + 2)} div (5^{-3})^x = (5^4)^{-1})
(5^{2 – 2x} times 5^{x + 2} div 5^{-3x} = 5^{-4})
(5^{(2 – 2x) + (x + 2) – (-3x)} = 5^{-4})
Equating bases, we have
(2 – 2x + x + 2 + 3x = -4)
(4 + 2x = -4 implies 2x = -4 – 4)
(2x = -8)
(x = -4)
There is an explanation video available below.