Answer:
[tex]27p^{26}[/tex]
Step-by-step explanation:
Let's start defining some properties about exponents.
In the properties, we use a,b,c where a,b,c ∈ IR.
[tex](a.b)^{c}=(a^{c}).(b^{c})[/tex] (I)
This means, that we can distribute the exponent respect a multiplication.
[tex](a^{b})^{c}=a^{(b.c)}[/tex] (II)
And finally
[tex](a^{b}).(a^{c})=a^{(b+c)}[/tex] (III)
Using this three properties we are going to solve the exercise :
[tex](3p^{4})^{3}.(p^{2})^{7}=(3^{3}).(p^{4})^{3}.(p^{14})[/tex]
We used properties (I) and (II)
[tex]3^{3}.(p^{4})^{3}.(p^{14})=27.(p^{12}).(p^{14})=27p^{26}[/tex]
The final step is to use property (II) again and the property (III)
