Question

Find the product.

(3p^4)^3 · (p^2)^7

Answer 1

`27p^(26)`

Explanation:

Let's start defining some properties about exponents.

In the properties, we use a,b,c where a,b,c ∈ IR.

`(a.b)^(c)=(a^(c)).(b^(c))` (I)

This means, that we can distribute the exponent respect a multiplication.

`(a^(b))^(c)=a^((b.c))` (II)

And finally

`(a^(b)).(a^(c))=a^((b+c))` (III)

Using this three properties we are going to solve the exercise :

`(3p^(4))^(3).(p^(2))^(7)=(3^(3)).(p^(4))^(3).(p^(14))`

We used properties (I) and (II)

`3^(3).(p^(4))^(3).(p^(14))=27.(p^(12)).(p^(14))=27p^(26)`

The final step is to use property (II) again and the property (III)

Answer 2

Explanation:

Good evening ,

Look at the photo below for the answer.