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help me solve this please i dont know where to start\(\[25^{-2}= \frac{5^{48/x}}{5^{26/x}\cdot 25^{17/x}}.\]\)

 Jun 18, 2020
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Let t = 1/x.

 

\(25^{-2} = \dfrac{5^{48t}}{5^{26t} \cdot 25^{17t}}\)

 

Rewrite 25^n into 5^(2n),

 

\(5^{-4} = \dfrac{5^{48t}}{5^{26t}\cdot 5^{34t}}\)

 

By law of indices,

 

\(5^{-4}= 5^{-12t}\)

 

Equating the powers would give t = 1/3, which means x = 3.

 Jun 18, 2020

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