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plz help $25^{-2}= \frac{5^{48/x}}{5^{26/x}\cdot 25^{17/x}}.$

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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

#1
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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