If $25^{1-x} \times 5^{x+2} \div \left(\frac{1}{125}\right)^x = 625^{-1}$, find the value of x.

Assessment: JAMB UTME - Mathematics - 2019 Subject: General Mathematics

Question 1 Report

x = -4

x = 2

x = -2

x = 4

Answer Details

$25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{- 1}$
$(5^{2})^{(1 - x)} \times 5^{(x + 2)} \div (5^{- 3})^{x} = (5^{4})^{- 1}$
$5^{2 - 2 x} \times 5^{x + 2} \div 5^{- 3 x} = 5^{- 4}$
$5^{(2 - 2 x) + (x + 2) - (- 3 x)} = 5^{- 4}$
Equating bases, we have
$2 - 2 x + x + 2 + 3 x = - 4$
$4 + 2 x = - 4 ⟹ 2 x = - 4 - 4$
$2 x = - 8$
$x = - 4$

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If \(25^{1-x} \times 5^{x+2} \div \left(\frac{1}{125}\right)^x = 625^{-1}\), find the value of x.

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