Simplify $ \frac{3^{9} \times p^{7}}{9^{3} \times p^{4}} $.


Given:

\( \frac{3^{9} \times p^{7}}{9^{3} \times p^{4}} \).

To do: 

We have to simplify \( \frac{3^{9} \times p^{7}}{9^{3} \times p^{4}} \).

Solution:

We know that,

$a^m \times a^n= a^{m+n}$

$\frac{a^m}{a^n}=a^{m-n}$

$\frac{3^{9} \times p^{7}}{9^{3} \times p^4} =\frac{3^{9} \times p^{7}}{(3^2)^{3} \times p^4}$

$=\frac{3^{9} \times p^{7}}{(3)^{2\times3} \times p^4}$

$=\frac{3^{9} \times p^{7}}{3^{6} \times p^4}$

$=3^{9-6}\times p^{7-4}$

$=3^3\times p^3$

$=(3p)^3$

Therefore,

$\frac{3^{9} \times p^{7}}{9^{3} \times p^4} =(3p)^3$.

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Updated on: 10-Oct-2022

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