JAMB Mathematics 2019 Paper

$25^{1 - x} \times 5^{x + 2} \div \left(\frac{1}{125}\right)^{x} = 625^{-1}$

$(5^2)^{(1 - x)} \times 5^{x + 2} \div (5^{-3})^{x} = (5^4)^{-1}$

$5^{2 - 2x} \times 5^{x + 2} \div 5^{-3x} = 5^{-4}$

$5^{(2 - 2x) + (x + 2) - (-3x)} = 5^{-4}$

Equating bases, we have

$2 - 2x + x + 2 + 3x = -4$

$4 + 2x = -4 \implies 2x = -4 - 4$

$2x = -8$

$x = -4$