Question

If 5³ⁿ ÷ 25 = 125, find the value of n.​

Answer 1

The answer is 40
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Answer 2

$\sf\huge\bold{Solution}$

$\sf\longmapsto \dfrac{ {5}^{3n} }{25} = 125$

$\sf\longmapsto \dfrac{ {5}^{3n} }{ {5}^{2} } = 125$

$\because$ Bases are same so,their powers gets subtracted.

Note: But when these terms are in multiplication we add their powers.

$\sf\longmapsto\dfrac{ {5}^{3n - 2} }{1} = {5}^{3}$

$\sf\longmapsto{5}^{3n - 2} ={5}^{3}$

Bases are same on both sides so ,it gets cancelled automatically.

$\sf\longmapsto3n - 2 = 3$

$\sf\longmapsto3n = 5$

$\sf\longmapsto \: n = \dfrac{5}{3}$

Check:

$\sf\longmapsto \dfrac{ {5}^{3 \times \dfrac{5}{3} } }{25}$

$\sf\longmapsto \dfrac{ {5}^{5} }{25}$

$\sf\longmapsto \dfrac{3125}{25} = 125$