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Cube Root Using Prime Factorisation

If 3x=270, ...

Question

If $3^{x} = 270$ , then find $3^{x - 3}$ .

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Solution

Given, $3^{x} = 270$ .
Now,
$3^{x - 3}$
$= \frac{3^{x}}{3^{3}}$
$= \frac{270}{27}$ [ Using value of $3^{x}$ ]
$= 10$ .

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