Question

Find the product. (3p^4)^3 · (p^2)^7

Answer 1

Answer:

$27p^{26}$

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.

$(a.b)^{c}=(a^{c}).(b^{c})$ (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

Answer:

Step-by-step explanation:

Good evening ,

Look at the photo below for the answer.