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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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